LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

©I  FT    OF 


C/ass 


THE  WINDMILL: 


ITS 


EFFICIENCY   AND    ECONOMIC   USE 


A  thesis  presented  to  the  Faculty  of  Cornell  University  for  the 
Degree  of  Doctor  of  Philosophy, 


BY 


EDWARD  CHARLES  MURPHY,  C.E.  and  M.S. 
Fellow  in  Civil  Engineering. 


UNIVERSITY 

OF 

SiUFOR 


WASHINGTON,  D.  C. 

GOVERNMENT  PRINTING  OFFICE 

1901 


CONTENTS. 


Introduction 

Classification  of  windmills 

Regulating  devices i 

Early  experiments 

Experiments  by  writer 

Scope  of  tests 

Pumping  mills 

Wells  near  Garden,  Kansas 

Pumps 

Instruments  and  methods 

Mills  tested 

Discussion  of  results  of  tests 

Relation  between  wind  velocity  and  strokes  of  pump. 

Useful  work 

Pressure-tank  system 

Comparison  of  three  pumping  Aermotors 

Useful  work  of  two  pumping  mills  in  a  given  time  __. 
Proper  load 


2006S? 


ILLUSTRATIONS. 


Page. 

PLATE  I.  Dutch  windmill  at  Lawrence,  Kansas.     14 

II.  Elevation  of  apparatus  used  by  Perry  in  wind- wheel  tests 20 

III.  View  of  mill  No.  2  (12-foot  Woodmanse  Mogul)  and  anemometer.  28 

IV.  View  of  mill  No.  3— 12-foot  Aermotor   30 

V.  View  of  mills  No.  4  (8-foot  Ideal)  and  No.  5  (8-foot  Aermotor)  _ . .  32 

VI.  Working  parts  of  mill  No.  6— 8- foot  Gem 40 

VII.  View  of  mill  No.  12— 14-foot  Ideal 42 

VIII.  View  of  mill  No.  13— 12-foot  Aermotor 42 

IX.  View  of  mill  No.  19— 12-foot  Gem. ..  44 

X.  A,  View  of  mill  No.  20 — 15|-foot  Jumbo;  B,  View  of  Defender  mill 

and  "water  elevator" : 46 

XI.  View  of  mill  No.  21— 12-foot  Halliday 46 

XII.  View  of  mill  No.  35— 8-foot  Dempster.. 52 

XIII.  View  of  mill  No.  42— 6-foot  Ideal 58 

XIV.  View  of  mill  No.  48— 30-foot  Halliday 60 

FIG.  1.  Section  of  common  European  post  windmill  mounted  on  central 

column 12 

2.  Early  form  of  head  of  European  tower  windmill 13 

3.  View  of  Gause  pump  ... - 24 

4.  Working  parts  of  Woodmanse  Mogul 26 

5.  Sectional  view  of  Woodmanse  pump 27 

6.  Diagram  showing  results  with  mill  No.  2 — 12-foot  Woodmanse 

Mogul 28 

7.  Working  parts  of  Aermotor 29 

8.  View  of  Stone  pump _ 30 

9.  Details  of  Stone  pump 31 

10.  Diagram  showing  results  with  mill  No.  3 — 12-foot  Aermotor 32 

11.  Diagram  showing  results  with  mill  No.  4 — 8- foot  Ideal    . 32 

12.  Diagram  showing  results  with  mill  No.  5 — 8-foot  Aermotor 33 

13.  Diagram  showing  results  with  mill  No.  9— 16-foot  Aermotor. 33 

14.  Working  parts  of  mill  No.  1 1— 12-foot  Ideal 38 

15.  Diagram  showing  results  with  mill  No.  11 39 

16.  Working  parts  of  Frizell  cylinder _  40 

17.  Diagram  showing  results  with  mill  No.  12 — 14-foot  Ideal. 41 

18.  Diagram  showing  results  with  mill  No.  19 — 12-foot  Gem 45 

19.  Diagram  showing  results  with  mill  No.  20— 15^- foot  Jumbo. 46 

20.  Working  parts  of  Halliday  mill 47 

21.  Diagram  showing  results  with  mill  No.  21— 12-foot  Halliday _ .  48 

22.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  30 — 16- 

foot  Irrigator ... 49 

23.  Diagram  showing  horsepower  of  mill  No.  30 50 

7 


8  ILLUSTRATION?. 

Page. 
FIG.  24.  Comparative  diagram  showing  results  with  mills  No.  35  (8-foot 

Dempster)  and  No.  36  (22i-foot  Eclipse) 53 

25.  Pump,  pressure- tank  and  hydraulic  regulator  of  mill  No.  37 — 12- 

foot  Woodmanse  Mogul _ ... 54 

26.  Diagram  showing  results  with  mill  No.  37 55 

27.  Comparative  diagram  showing  results  with  mills  No.  38  (10-foot 

wooden  Woodmanse)  and  No.  48  (30- foot  wooden  Halliday ) 56 

28.  View  of  mill  No.  43— 10-foot  Perkins 58 

29.  Working  parts  of  mill  No.  51— 8-foot  Monitor  .... 62 

30.  Diagram  showing  relation  between  horsepower  and  wind  velocity 

for  five  12-foot  mills... .."         66 

81.  Diagram  showing  relation  between  horsepower  and  wind  velocity 

for  four  8-foot  mills . .  67 


THE  mmill.  ITS  EFFICIENCY  AND  ECONOMIC  USE. 

PART   I. 


By  EDWARD  CHARLES  MURPHY. 


INTRODUCTION. 

History  does  not  record  the  name  of  the  person  who  invented  the 
windmill,  nor  give  the  date  of  the  invention.  The  belief  that  wind- 
mills were  used  by  the  Romans  is  not  well  authenticated,  and  their 
use  by  the  Bohemians  in  718  is  doubted.  It  is  quite  clear,  however, 
that  they  were  used  in  France  and  Italy  in  the  twelfth  century  for 
grinding  corn,  and  that  they  were  used  in  Holland  in  the  fifteenth 
century  for  pumping  water  over  the  dikes  into  the  sea. 

Mr.  John  Burnham,  of  Connecticut,  is  said  to  be  the  inventor  of 
the  American  windmill.  Mr.  L.  H.  Wheeler,  an  Indian  missionary, 
patented  the  Eclipse  mill  in  1867.  The  first  steel  mill  was  the  Aer- 
motor,  invented  by  Mr.  T.  O.  Perry  in  1883. 

The  common  European  windmill,  shown  in  section  in  figs.  1  and  2, 
differs  much  in  appearance  from  the  American  mill.  The  wind  wheel 
of  the  European  mill  has  usually  four  long  wooden  arms,  to  each  of 
which  is  attached  a  sail,  against  which  the  wind  presses.  The  sails 
consist  of  a  framework,  on  which  canvas  is  stretched,  usually  forming 
a  warped  surface,  the  angle  with  the  plane  of  the  arms  (called  the 
angle  of  weather)  being  about  7°  at  the  outer  end  and  18°  at  the  inner 
end.  The  length  of  sail  was  usually  about  five-sixths  the  length  of 
the  arm,  the  width  of  the  outer  end  one-third  the  length,  and  the 
width  of  the  inner  end  one-fifth  the  length.  The  sail  area  is  seen  to 
be  small  compared  with  the  wind  area  or  zone  containing  the  sails. 
The  arms  were  sometimes  60  feet  long.  The  American  wooden  mill  is 
much  smaller  and  more  compact  than  the  European  mill.  It  has  six 
or  eight  arms,  to  which  is  attached  a  framework  carrying  many  small 
sails.  These  sails  are  usually  3  or  4  feet  long,  3  or  4  inches  wide  at 
the  outer  end,  and  1  to  3  inches  wide  at  the  inner  end,  and  are  set  at 
an  angle  of  30°  to  40°  to  the  plane  of  the  wheel.  For  large  wheels 
these  sails  are  arranged  in  two  or  more  concentric  rings.  The  Ameri- 

11 


THE    WINDMILL. 


can  steel  mill  differs  principally  from  the  wooden  mill  in  that  it  has 
larger  and  fewer  sails  for  a  given  size  of  mill,  its  sails  are  curved 
instead  of  plane,  and  it  offers  less  resistance  to  the  passage  of  the  air 
over  the  back  of  the  sails.  In  the  sails  of  the  steel  mill  there  is  seen 
to  be  a  partial  return  to  those  of  the  European  mill. 


FIG.  1.— Section  of  common  European  post  windmill  mounted  on  central  column. 

CLASSIFICATION   OF   WINDMILLS. 

Windmills  may  be  divided  into  two  general  classes — paddle  wheel 
and  sail  wheel.  The  Jumbo  shown  in  PI.  XVI,  B  (Part  II),  and  Little 
Giant  No.  56,  described  on  pages  125  to  127,  Part  II,  are  good  illus- 
trations of  the  first  class.  In  both  of  these  mills  the  sails  move  with 
the  wind,  and  it  is  necessary  to  have  a  shield,  or  a  method  of  feathering 


MURPHY.] 


CLASSIFICATION    OF    WINDMILLS. 


13 


the  sails,  in  order  to  keep  the  wind  from  striking  them  when  they  are 
moving  in  a  direction  opposite  to  that  of  the  wind.  In  the  Jumbo  the 
axis  of  the  wheel  is  horizontal,  in  the  Little  Giant  it  is  vertical;  but 
the  wind  acts  on  the  sails  of  both  in  substantially  the  same  way. 
The  air  acts  with  full  pressure  on  only  one  sail  of  the  Jumbo  at  any 
one  time,  and  on  half  the  sails  it  has  no  action,  or  only  negative 
action. 

In  the  sail- wheel  mill  (fig.  1,  Part  I,  and  PL  XV,  Part  II)  the  wheel 
moves  at  right  angles  to  the  direction  of  the  wind,  instead  of  in  the 
same  direction,  as  in  the  paddle-wheel  mill.  The  wind  acts  with  a 


FIG.  2.— Early  form  of  head  of  European  tower  windmill. 

certain  pressure  011  all  of  the  sails  all  of  the  time.  The  circumference 
velocity  of  the  sail  wheel  may  be  two  or  more  times  greater  than  the 
velocity  of  the  wind  that  drives  it,  but  the  circumference  velocity  of 
the  paddle  wheel  is  always  less  than  the  velocity  of  the  wind  that  drives 
it.  The  sails  of  the  sail- wheel  mill  must  be  placed  at  an  angle  with 
the  plane  of  the  wheel,  so  that  the  wind  will  press  on  them;  but  the 
sails  of  the  paddle-wheel  mill  may  be  IL  the  plane  of  the  axis  of  the 
wheel. 

For  greatest  pressure  on  the  sails  of  a  sail-wheel  mill  the  axis  of  the 


14  THE    WINDMILL.  [NO. 41. 

wheel  must  be  parallel  to  the  direction  of  the  wind.  It  is  necessary, 
then,  for  the  wheel  to  change  its  direction  as  the  wind  changes.  In 
the  German  or  post  mill  the  whole  building,  as  well  as  the  wheel,  can 
be  turned  around  on  a  post  by  hand.  In  the  tower  or  Dutch  mill  the 
upper  part  only  of  the  mill  turns  with  the  wheel.  This  is  accomplished 
by  hand  in  the  mill  shown  in  fig.  1,  and  by  an  auxiliary  windmill  in 
the  mill  shown  in  fig.  2.  In  the  American  mills  the  upper  part  only 
turns  on  a  turntable,  which  is  usually  on  rollers  or  balls.  This  is 
accomplished,  first,  by  the  pressure  of  the  wind  on  a  long  rudder 
vane  extending  out  behind  the  mill,  and  in  some  mills  by  a  side  vane 
as  well;  or,  second,  by  the  pressure  of  the  wind  on  the  wheel  itself, 
which  is  placed  on  the  opposite  side  of  the  tower,  as  in  fig.  46,  Part 
II ;  or,  third,  by  side  wheels,  as  in  mill  No.  52,  fig.  50,  Part  II. 

REGULATING  DEVICES. 

The  wind  is  constantly  changing  in  velocity  as  well  as  in  direction, 
and  if  the  load  on  the  mill  is  constant  the  speed  of  the  mill  and  of 
the  machine  which  it  operates  will  change  with  it.  If  the  speed  is  to 
be  kept  'nearly  constant,  some  device  is  needed  to  reduce  the  wind 
pressure  on  the  wheel  when  the  wind  velocity  reaches  a  certain 
amount.  In  the  European  mill  there  are  two  methods  of  doing  this, 
viz,  by  means  of  a  brake  or  friction  rings  and  by  changing  the  sail 
area.  The  latter  is  accomplished  by  rolling  or  unrolling  the  canvas 
sails  by  hand  or  automatically.  In  the  American  mill  the  speed  is 
regulated  by  changing  the  sail  area  in  one  of  three  ways :  (a)  By  sec- 
tions of  the  wheel  revolving  about  an  axis  which  places  each  sail  at 
an  angle  to  the  direction  of  the  wind  less  than  90°,  as  in  fig.  36,  Part 
II ;  (b)  by  placing  the  axis  of  the  wind  wheel  eccentric  to  the  axis  of  the 
tower,  so  that  the  wind  pressure  on  the  wheel  will  cause  it  to  revolve 
around  the  axis  of  the  tower;  and  (c)  by  the  wheel  moving  natu- 
rally around  the  axis  of  the  tower  in  the  direction  in  which  it  is 
revolving.  This  turning  action  around  the  axis  of  the  tower  is  counter- 
acted by  a  spring  or  a  weight,  or,  as  we  commonly  say,  "the  wheel  is 
held  in  the  wind  "  by  a  spring  or  a  weight.  A  weight  is  better  than 
a  spring,  for  by  moving  it  out  or  in  any  desired  pull  can  be  placed  on 
the  wheel.  A  spring  can  not  easily  be  adjusted  and  may  lose  some  of 
its  tension.  The  first  method  of  regulation,  called  the  centrifugal- 
governor  method,  is  used  in  the  Halliday  mill  (fig.  20)  and  in  the 
Althouse-Wheeler  mill  (fig.  36,  Part  II).  The  second  method  is  illus- 
trated in  the  Aermotor  (fig.  33,  Part  II),  which  shows  the  axis  of  the 
wheel  eccentric  to  the  axis  of  the  tower  by  4.5  inches.  It  also  shows 
the  spring  which  holds  it  in  the  wind.  This  spring  also  resists  the 
action  of  the  load,  which  tends  to  turn  the  wind  wheel  out  of  the  wind. 
The  third  method  is  illustrated  by  the  Woodmanse  mill. 


U.   S.    GEOLOGICAL  SURVEY 


WATER-SUPPLY  PAPER  NO.  41       PL.    I 


DUTCH   WINDMILL  AT   LAWRENCE,   KANSAS. 


MURPHY.]  EARLY    EXPERIMENTS.  15 

EARTHY  EXPERIMENTS. 

Smeatori's  experiments. — The  first  experiments  of  which  we  have 
any  record  were  made  by  John  Smeaton,  an  English  engineer,  and 
published  in  1755  to  1763. 1  These  experiments  were  made  on  model 
windmills  of  the  European  type,  for  the  purpose  of  determining  the 
best  shape  of  sail  for  a  given  sail  area.  The  models  each  had  four 
arms  21  inches  long.  For  one  set  of  tests  the  sails  were  5.6  inches 
broad  and  18  inches  long,  giving  an  area  of  403  square  inches.  In 
another  set  of  tests  the  sails  were  18  inches  long,  5.6  inches  wide  at 
the  inner  end  and  8.4  inches  wide  at  the  outer  end,  with  an  area  of  504 
square  inches.  The  sails  were  either  plane  or  warped  at  various  angles. 
These  mills  were  worked  by  moving  the  windmill  around  in  a  circle  of 
5-j-  feet  radius,  in  still  air,  instead  of  placing  them  on  a  tower  and  allow- 
ing the  natural  wind  to  drive  them.  The  wheel  was  moved  around  in 
this  circle  by  means  of  a  cord  wound  on  a  drum  on  a  vertical  shaft, 
the  horizontal  arm  which  held  the  wheel  being  fastened  to  this  shaft. 
The  work  done  by  the  wheel  in  a  given  time  was  measured  by  observing 
the  length  of  string  wound  on  the  shaft  of  the  wheel,  a  weight  of 
known  size  being  attached  to  the  end  of  the  string.  The  velocity  of 
the  wind,  which  was  assumed  to  be  the  velocity  of  the  end  of  the  arm 
where  the  wheel  was  attached  to  it,  varied  from  4£  to  8f  "feet  a  second, 
or  from  2.9  to  6  miles  an  hour. 

It  will  be  noticed  that  these  wheels  are  only  3.5  feet  in  diameter, 
that  they  were  moved  in  a  circle  only  5.5  feet  in  diameter,  and  that 
wind  velocities  or  wheel  velocities  were  small  and  of  only  a  limited 
range — from  about  3  to  6  miles  an  hour.  Smeaton  draws  the  follow- 
ing conclusions  from  his  experiments : 

(1)  The  velocity  of  the  windmill  sails,  whether  unloaded,  or  loaded  so  as  to  pro- 
duce a  maximum,  is  nearly  as  the  velocity  of  the  wind:  their  shape  and  position 
being  the  same. 

(2)  The  load  at  the  maximum  is  nearly,  but  somewhat  less  than  as  the  square 
of  the  velocity  of  the  wind:  the  shape  and  position  of  the  sails  being  the  same. 

(3)  The  effects  of  the  same  sails  at  a  maximum  are  nearly  but  somewhat  less 
than  as  the  cubes  of  the  velocity  of  the  wind. 

(4)  The  load  of  the  same  sails  at  the  maximum  is  nearly  as  their  squares  and 
their  effects  as  the  cubes  of  their  number  of  turns  in  a  given  time. 

(5)  When  the  sails  are  loaded  so  as  to  produce  a  maximum  at  a  given  velocity 
of  the  wind,  and  the  velocity  of  the  wind  increases,  the  load  remaining  the  same: 
first,  the  increase  of  effect,  when  the  increase  of  the  velocity  of  the  wind  is  small, 
will  be  nearly  as  the  squares  of  those  velocities;  secondly,  when  the  velocity  of 
the  wind  is  doubled,  the  effects  will  be  nearly  as  10  to  27.5;  but,  thirdly,  when  the 
velocities  compared  are  more  than  double  of  that  where  the  given  load  produces 
a  maximum,  the  effects  increase  nearly  in  a  simple  ratio  of  the  velocity  of  the 
wind. 

(6)  If  sails  are  of  similar  figure  and  position,  the  number  of  turns  in  a  given 
time  will  be  reciproca'ly  as  the  radius  or  length  of  the  sail. 


Philos.  Trans.  Royal  Soc.  London,  1756-1763. 


16  THE    WINDMILL.  [NO.  41. 

(7)  The  load  afc  a  maximum  that  sails  of  a  similar  figure  and  position  will  over- 
come at  a  given  distance  from  the  centre  of  motion,  will  be  as  the  cube  of  the 
radius. 

(8)  The  effects  of  sails  of  similar  figure  and  position  are  as  the  square  of  the 
radius. 

(9)  The  velocity  of  the  extremity  of  Dutch  sails,  as  well  as  of  enlarged  sails,  in 
all  their  usual  positions,  when  unloaded,  or  loaded  to  a  maximum,  is  considerably 
quicker  than  the  velocity  of  the  wind. 

Regarding  the  ratio  of  the  sail  area  to  the  wind  area  or  zone  contain- 
ing the  sails,  he  found  that  where  the  ratio  was  greater  than  7  to  8  the 
power  of  the  mill  was  decreased  instead  of  increased.  Regarding  the 
proper  shape  of  sail,  he  found  that  the  warped  sail  was  more  effective 
than  the  plane  sail.  He  also  found  the  following  six  angles  of  weather 
at  equal  distances  from  the  shaft  outward  advantageous:  70°,  71°,  72°, 
74°,  77.5°,  and  83°.  He  states  that  a  difference  of  two  or  three  degrees 
in  the  angles  of  impact  makes  little  difference  in  the  power  of  the 
mill. 

Coulomb's  experiments. — C.  A.  Coulomb,  a  French  engineer,  made 
some  tests  of  the  work  done  by  a  Dutch  windmill  used  for  extracting 
oil  from  rape  seed  at  Lille,  in  Flanders.  His  observations  were  pub- 
lished in  1821. 1  The  mill  was  70.2  feet  in  diameter.  It  had  four 
warped  canvas  sails,  each  28.7  feet  long  and  6.6  feet  wide;  the  width 
of  canvas  was  5.5  feet.  The  angle  which  the  plane  of  sail  made  to 
the  plane  of  the  wheel  varied  from  30°  at  the  inner  end  to  12°  at  the 
outer  end.  The  wind  velocity  was  measured  by  the  use  of  feathers 
carried  along  by  the  wind.  Two  men  were  stationed  150  feet  apart, 
on  slight  elevations,  to  note  the  time  required  for  each  feather  to  pass 
over  this  distance.  The  velocity  of  the  wind  striking  the  wind  wheel 
was  assumed  to  be  that  found  from  these  feathers.  In  a  14.9-mile 
wind,  and  with  the  load  ordinarily  used,  he  found  that  the  wheel  made 
13  revolutions  per  minute  with  all  the  canvas  spread.  From  these 
data  he  figured  the  useful  work  done  by  the  mill  per  minute  to  be 
232,388  foot-pounds  and  the  useless  work  expended  in  shock  of  stamp- 
ers and  friction  to  be  37,310  foot-pounds,  or  a  total  of  269,698  foot- 
pounds, equal  to  8.17  horsepower. 

Coulomb  did  not  consider  this  a  complete  or  satisfactory  test  of 
this  mill.  He  did  not  control  the  working  of  the  mill,  but  simply 
observed  what  it  did  when  handled  by  the  miller  who  extracted  the 
oil.  He  tried  to  induce  the  owner  to  permit  him  to  use  the  mill  for  a 
time  for  experimental  purposes,  but  did  not  succeed. 

It  will  be  seen  from  what  follows  that  even  if  we  assume  the  wind 
velocity  to  be  correctly  measured,  this  test  does  not  necessarily  show 
the  power  of  the  mill,  for  we  do  not  know  that  the  load  used  was  the 
proper  load  for  the  wind  velocity.  It  shows  what  the  mill  was  doing, 
not  what  it  might  do  under  a  better  loading. 

i  Theorie  de  Machines  Simple,  by  G.  A.  Coulomb.    Paris,  1831. 


MURPHY.] 


EARLY    EXPERIMENTS. 


17 


Griffiths' s  experiments.^ — In  1891-92  Mr.  J.  A.  Griffiths  made  tests 
of  six  windmills  used  for  raising  water,  with  the  following  results: 

Results  of  windmill  tests  by  J.  A.  Griffiths. 


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eg 

£,  O 

0  ftto 

'a;  ^fl 

•s5h 

o 

ox 

H 

O 

^ 

s 

00 

^ 

J 

^ 

w 

^ee^. 

Feet. 

Sqft 

0            / 

Tn. 

/W. 

Feet 

Ft.-lbs. 

Miles. 

Rev. 

1 

Toowoomba 

22.3 

8.3 

39.20 

18    47 

5 

6.75/ 

25 

120 

4.3 

5.0 

0.018 

100 

480 

7.0 

6.8 

0.098 

v 

Stover 

11.5 

4.5 

104.  0 

43 

3 

4{ 

29.2 

29.2 

5.8 

13.0 

0.011 

\ 

61.2 

61.2 

6.5 

13.3 

0.  025 

B 

Perkins  

16.0 

6.0 

201.0 

36 

3 

10.75 

39.0 

105.0 

6.0 

7.5 

0.024 

4 

Althouse  -Wheeler  . 

14.2 

4.5 

157.0 

30 

3 

clO 

66.3 

166.0 

7.0 

12.6 

0.065 

6 

do        

10.2 

3.8 

81.0 

28 

8 

4f 

38.7 

51.0 

8.5 

20.5 

0.  028 

6 

Carlyle 

9  8 

4.2 

80.0 

50 

3 

4 

30.7 

30.7 

6.0 

12.5 

0.012 

a  These  pump  loads  have  been  computed  for  comparison  of  these  results  with  others. 
b  At  maximum  efficiency. 
^  c  Pump  is  double  acting;  this  is  twice  the  length  of  stroke. 

No.  1  was  a  22.5-foot  wooden  mill,  with  20  warped  sails  each  87  by 
36  by  9  inches,  the  weather  angle  at  the  outer  end  being  18°  47'  and 
at  the  inner  end  40°  20'.  It  worked  a  direct-acting  single-stroke  pump 
having  a  5-inch  cylinder  and  6.75  inches  stroke.  Two  lifts  were  used, 
one  of  25  feet  and  the  other  of  100  feet. 

No.  2  was  a  12-foot  Stover  wooden  mill,  having  a  wind  wheel  some- 
what like  that  of  mill  No.  38.  It  had  112  sails,  each  43  by  3.75  by  1.5 
inches,  set  at  an  angle  of  43°  to  the  plane  of  the  wheel.  It  worked  a 
direct-acting  single-stroke  pump  having  a  3-inch  cylinder  and  4  inches 
stroke.  The  lifts  were  29.2  and  61.2  feet. 

No.  3  was  a  16-foot  Perkins  solid  wood  wheel,  the  wind  wheel  hav- 
ing 160  sails,  each  60  by  4  by  1.5  inches,  set  at  an  angle  of  36°  to  the 
plane  of  the  wheel.  It  worked  a  direct- acting  double-stroke  pump 
having  a  3-inch  cylinder  and  5.375  inches  stroke.  The  lift  was  39 
feet. 

No.  4  was  a  14-foot  Althouse- Wheeler  wooden  sectional  mill,  the 
wind  wheel  having  104  sails,  each  48  by  4  by  1.5  inches,  set  at  an  angle 
of  30°  to  the  plane  of  the  wheel.  It  worked  a  direct-acting  double- 
stroke  pump  having  a  3-inch  cylinder  and  5  inches  stroke.  The  lift 
was  66.3  feet. 

No.  5  was  a  10-foot  Althouse- Wheeler  wooden  sectional  mill.  The 
wind  wheel  had  84  sails,  each  38  by  3.75  by  1.5  inches,  set  at  an  angle 
of  28°  to  the  plane  of  the  wheel.  It  worked  a  direct-acting  single- 
stroke  pump  having  a  3-inch  cylinder  and  4.625  inches  stroke.  The 
lift  was  38.7  feet. 

No.  6  was  a  10-foot  Carlyle  iron  mill.  It  had  7  somewhat  spoon- 
shaped  sails,  each  having  a  spout-like  extension  through  which  the 


1  Windmills  for  raising  water,  by  J.  A.  Griffiths:  Proc.Inst  Civ.  Eng.,  Vol.  CXIX,  p.  321, 

IRR  41—01 2 


18  THE    WINDMILL.  [NO. 41. 

air  flowed.     It  worked  a  direct -acting  single-stroke  pump  having  a 
3-inch  cylinder  and  4  inches  stroke.     The  lift  was  30.7  feet. 

The  wind  velocity  was  measured  with  the  "  f "  wind  gage,  which 
was  either  on  a  tower  near  by  or  on  an  arm  projecting  as  far  as  pos- 
sible to  windward.  It  appears  that  it  was  necessary  to  be  near  the 
gagp  in  order  to  read  the  velocity,  which  would  indicate  a  possible 
error  in  wind  velocity  and  some  interference  with  the  wind  striking 
the  wind  wheel.  The  range  of  wind  velocities  is  not  stated,  and  not 
more  than  two  loads  were  used  in  any  case. 

These  results  will  be  compared  with  others  further  on. 

King's  experiments}- — Prof.  F.  H.  King  conducted  a  series  of  experi- 
ments with  a  16-foot  geared  Aermotor,  covering  a  period  of  one  year — 
from  March  6,  1897,  to  March  6,  1898.  This  mill  was  used  to  work 
one  or  more  of  four  pumps:  (1)  A  reciprocating  piston  pump  with  a 
14-inch  cylinder  and  9  inches  stroke;  (2)  a  bucket  pump  having  a 
normal  capacity  of  120  gallons  per  minute;  (3)  a  No.  2  Gould  centrif- 
ugal pump;  and  (4)  the  smallest  size  Menge  pattern  centrifugal  pump. 
The  bucket  pump  was  used  nearly  all  of  the  time.  The  reciprocating 
piston  pump  was  used  occasionally  by  itself  and  part  of  the  time  with 
the  bucket  pump,  when  the  wind  velocity  was  strong  enough  to  carry 
both.  The  Menge  was  used  occasionally  with  the  piston  pump  and  the 
bucket  pump,  when  the  wind  velocity  was  strong  enough  to  carry  all. 

There  was  no  automatic  device  for  throwing  into  or  out  of  use  any 
of  these  pumps.  It  was  necessary  to  do  this  by  hand,  so  that  a  part 
of  the  time  the  load  on  the  mill  was  not  suited  to  the  wind  velocity. 
This  can  be  seen  from  the  record.  For  example,  on  February  10,  from 
1  to  7  p.  m.,  the  wind  velocity  varied  from  9  to  12  miles  an  hour  and 
8.6  tankfuls  of  water  were  pumped,  while  on  June  1,  from  8  a.  m.  to 
4  p.  m.,  the  wind  velocity  varied  from  11  to  15  miles  an  hour,  and  not 
a  tankful  was  pumped.  The  report  gives  the  number  of  tankfuls  of 
141.2  cubic  feet  which  were  lifted  12.85  feet  each  hour  during  the  year, 
and  some  interesting  conclusions  drawn  from  these  records. 

Professor  King  has  also  made  some  tests  of  this  mill  with  a  Prony 
friction  brake.  The  results  of  these  tests,  and  the  indicated  horse- 
powers computed  from  them,  are  as  follows : 

1  Bull.  No.  68,  Wisconsin  Agricultural  Experiment  Station. 


MURPHY.] 


EARLY    EXPERIMENTS. 

Results  of  tests  of  16-foot  geared  Aermotor. 


19 


Wind 
velocity 
per 
hour. 

Direction 
of  wind. 

Indicated 
horse- 
power. 

Average 
wind 
velocity. 

Average 
horse- 
power. 

Barometer. 

Tempera- 
ture. 

Miles. 
8.4 

12.0 

sw. 

0.2715 
0.5791 

Miles. 

8.4 
} 

0.2715 

Inches. 
29.40 
(     29.  36 

Degrees. 
0.0 
0.5 

12.4 

0.7230 

I    12.33 

0.  5858 

29.  36 

0.5 

12  6 

0.  4553 

) 

29.36 

0.25 

13.2 
14.6 
14.6 

sw. 
sw. 

0.6213 
0.  7343 
0.9449 

13.2 

1     14.68 

0.6213 
0.  8602 

29.40 
29.36 
29.40 

0.5 
-0.5 
0.5 

14.8 
18.6 
18.8 
21.2 
21.6 
21.6 
21   8 

sw. 
NW. 

sw. 
sw. 
w. 

N. 

NW 

0.9016 
2.054 
1.692 
2.593 
3.715 
3.227 
2  597 

J 

j    18.70 

21.55 

1.873 
3.033 

29.40 
28.86 
29.40 
29.40 
29.06 
28.86 

1.0 
9.0 
1.0 
1.5 
-2.0 
7.0 

22.0 
22.0 

22  2 

W. 

w. 

NW 

4.326 
4.236 
2  394 

22.06 

3.  652 

{29.09 
29.04 

1.0 
-2.0 

23.0 
23.0 
24  0 

W. 

w. 

3.842 
4.151 
5  983 

I    23.  00 

3.996 

29.07 
1    29.05 

/    28  75 

-1.0 
-1.0 
6.8 

24.6 
25.2 
27.3 
27.0 

39.0 
40.0 

w. 
w. 

N. 
W. 

N. 

3.554 

4.882 
4.092 
4.850 
5.  953 
5.971 

j    24.  30 
25.2 
I    27.16 

39.0 
40.0 

4.768 
4.882 
4.471 

5.953 
5.971 

\     29.  09 
29.09 
/    28.  66 
1     29.10 
"    28.69 
28.69 

1.5 

1.5 
6.3 
1.5 
6.5 
6.3 

This  mill  is  similar  to  our  16-foot  Aermotor  No.  44,  described  in  Part 
II.  It  will  be  seen  later  that  the  power  found  by  Professor  King  is  much 
greater  than  we  have  found  it  for  high  wind  velocities.  The  probable 
reason  for  this  difference  will  be  discussed  later.  It  may  be  stated  here, 
however,  that  Professor  King  measured  the  wind  velocity  with  an 
anemometer  in  a  fixed  position  40  feet  due  east  of  the  windmill,  and 
it  will  be  seen  that  the  wind  was  from  the  west,  northwest,  or  south- 
west nearly  all  of  the  time  when  the  brake  tests  were  being  made. 
(The  wind  came  from  the  north  around  by  the  east  to  the  south  only 
three  times  while  the  brake  tests  were  in  progress. )  The  revolving 
wheel  must  have  interfered  with  the  running  of  the  anemometer  and 
caused  it  to  show  a  less  wind  velocity  than  really  existed. 

Professor  King  also  determined  the  work  done  by  the  mill  in  grind- 
ing corn.  The  power  of  the  mill  in  a  given  wind  velocity  can  not, 
however,  be  judged  from  these  tests,  since  the  grinder  load  was 
probably  not  suited  to  all  wind  velocities. 


20 


THE    WINDMILL. 
Results  of  brake  tests  of  16-foot  geared  Aermotor. 


[NO.  41. 


Wind  velocity  per  hour. 

Indicated 
horse- 
power. 

Wind  velocity  per  hoxir. 

Indicated 
horse- 
power. 

8  miles        

0.25 

26  miles  .  .  .  

4.82 

10  miles 

0.40 

28  miles 

5  14 

12  miles 

0.56 

30  miles  .  . 

5  40 

14  miles          .  .       

0.78 

32  miles.  

5.61 

16  miles      ._ 

1.08 

34  miles  

5.76 

18  mUes        ..     

1.62 

36  miles  ...      ... 

5.87 

20  miles 

2.39 

38  miles 

5.95 

22  miles 

3.31 

40  miles 

5.97 

24  miles 

4.31 

Perry's  experiments. — From  June,  1882,  to  September,  1883,  Mr. 
T.  O.  Perry  made  experiments  with  61  windmills,  each  5  feet  in 
diameter.  The  results  were  published  in  1889. 1  Mr.  Perry's  methods 
were  similar  to  those  employed  by  Smeaton — he  used  small  wheels 
moved  against  still  air  in  a  circle  of  14  feet  radius.  His  experiments 
were  made  on  a  much  larger  scale  than  Smeaton's,  however,  and  his 
apparatus  was  more  perfect.  Smeaton  used  wheels  of  European  type; 
Mr.  Perry  used  those  of  American  type.  PL  II  is  an  elevation  of  Mr. 
Perry's  apparatus,  showing  the  wheel  as  it  revolved  about  the  vertical 
shaft,  driven  by  an  80-horsepower  engine.  The  power  was  measured 
by  means  of  a  Prony  friction  brake  placed  on  a  brass  cylinder  on  the 
wind- wheel  shaft.  In  order  to  eliminate  the  effect  due  to  differences 
in  the  condition  of  the  air,  and  get  results  comparable  with  one 
another,  Mr.  Perry  used  one  of  his  wheels  as  a  standard  with  which 
to  compare  the  others.  After  the  best  load  for  a  wheel  had  been 
obtained,  comparative  tests  were  made  with  this  one  and  with  the 
standard  wheel,  by  trying  first  one  wheel  and  then  the  other  until 
several  measurements  of  each  had  been  taken.  The  final  result  of 
each  wheel  was  the  average  of  eight  or  ten  measurements. 

In  comparing  Smeaton's  results  with  his  own,  Mr.  Perry  writes: 

We  were  not  able  to  obtain  the  best  results  with  weather  angles  as  small  as 
Smeaton's  in  any  of  our  wheels.  Nor  did  our  sail  speeds,  as  compared  with  wind 
velocity,  nearly  approach  the  speeds  obtained  by  Smeaton.  Even  our  unloaded 
wheels  did  not  show  the  sail  speed  attained  by  the  best  of  Smeaton's  when  loaded 
for  maximum  work.  *  *  *  Our  loads  at  the  maximum  of  work  were  sma'ler 
as  compared  with  the  greatest  loads,  and  the  speed  of  revolutions  at  maximum 
work  as  compared  with  the  speeds  of  unloaded  wheels,  were  smaller  for  our  mills 
than  for  Smeaton's. 

He  states,  however,  that  the  general  conclusions  drawn  by  Smeaton 
(see  pages  15  to  16)  were  substantially  confirmed  by  his  experimonis. 
The  difference  between  his  results  and  Smeaton's  lie  attributes  to  the 
differences  in  the  mills  used. 


Water-Supply  and  Irrigation  Paper  U.  S.  Geol.  Survey  No.  20. 


MURPHY.]  WRITER'S  EXPERIMENTS.  21 

Some  of  Mr.  Perry's  conclusions  are  as  follows: 

(1)  There  is  nothing  gained  by  having  the  sail  area  more  than  seven- 
eighths  of  the  wind  area,  and  there  is  little  gained  by  having  it  more 
than  three-fourths  of  the  latter  area. 

(2)  That  the  power  varies  as  the  cube  of  the  wind  velocity. 

(3)  That  the  load  for  maximum  power  varies  as  the  square  of  the 
wind  velocity. 

(4)  That  the  speed  of  the  unloaded  wheel  increases  somewhat  faster 
than  the  wind  velocity. 

(5)  That  the  best  speed  for  most  of  his  wheels  was  about  0.55  per 
cent  of  the  unloaded  speed. 

(6)  That  the  conical  deflector  at  the  center  of  the  wheel  does  not 
increase  the  power. 

(7)  That  obstructions  on  the  back  of  sails  greatly  reduce  the  power 
of  the  mill. 

(8)  That  the  speed  of  wheel  No.  48  was  increased  48  per  cent  by 
removing  the  strip  from  the  back  of  each  sail. 

(9)  That  a  deflector  in  front  of  the  wheel  increased  the  speed  of  a 
slow-moving  wheel. 

(10)  That  a  deflector  in  front  of  the  wheel  did  not  increase  the  speed 
of  a  rapidly  moving  wheel. 

(11)  That  a  mast  offers  more  obstruction  in  front  of  a  wheel  than 
behind  it. 

EXPERIMENTS  BY  WRITER. 

The  tests  of  wind  wills  described  in  the  following  pages  were  begun 
by  the  writer  in  the  summer  of  1895.  They  wrere  continued  during 
the  summer  of  1896,  Avith  much  better  facilities  than  during  the  pre- 
vious season.  The  results  obtained  to  that  time  were  published  in 
Water-Supply  and  Irrigation  Paper  No.  8,  entitled  Windmills  for 
Irrigation.  Since  then  the  work  has  been  continued  as  time  could 
be  spared — mainly  during  a  portion  of  three  summer  vacations. 
The  work  of  the  summer  of  1896  was  confined  mainly  to  pump- 
ing mills.  The  tests  show  what  each  windmill  and  its  pump  were 
actually  doing  under  certain  conditions  of  load,  lift,  etc.  They  do 
not  show  what  the  mill  might  do  under  other  conditions.  It  was  evi- 
dent that  the  useful  work  of  a  mill  varied  with  its  load  and  the 
efficiency  of  the  pump.  The  latter  could  not  well  be  ascertained.  It 
wTas,  therefore,  thought  best  to  confine  the  tests  principally  to 
power  mills,  in  which  the  unknown  factor  of  pump  efficiency  is  not 
present,  and  where  the  load  on  the  mill  can  easily  be  varied.  This 
has  enlarged  the  scope  of  the  work,  making  it  cover  windmills  for 
power  as  well  as  those  for  irrigation. 

Many  of  our  tests  of  pumping  mills  were  made  in  the  vicinity  of 
Garden,  Kansas.  Perhaps  nowhere  in  the  United  States  is  irrigation 
from  wells  by  the  use  of  windmills  carried  to  the  same  extent  as  there, 


22  THE    WINDMILL.  [NO.  41. 

where  may  be  found  hundreds  of  windmill  pumping  plants  furnishing 
water  to  irrigate  from  1  to  15  acres  each  and  lifting  from  3  to  14.5 
quarts  per  stroke  to  a  height  of  from  10  to  45  feet,  as  well  as  large 
steel  mills  running  day  and  night,  when  the  wind  is  strong  enough, 
and  working  pumps  of  the  best  kind. 

SCOPE  OF  TESTS. 

There  are  many  makers  of  American  windmills,  and  with  the  great 
variety  of  mills  in  use — no  two  are  alike,  though  in  some  cases  the 
difference  is  slight — it  was  impossible  to  test  a  mill  of  each  type.  It 
was  our  purpose  to  test  only  the  mills  that  were  in  good  working  order 
and  subject  to  good  wind  exposure,  and  which  would  add  new  data  to 
that  already  obtained  or  confirm  in  some  particular  that  previously 
secured.  In  some  cases  two  or  more  mills  of  the  same  size  and  make 
were  tested  to  show  as  far  as  possible  the  effect  of  pump,  well,  etc. 
on  the  useful  work.  The  parts  of  mill  and  pump  on  which  the  power 
depends  were  carefully  measured.  The  temperature  and  barometric 
pressure  were  observed  in  each  case  and  the  mean  given.  The  dis- 
charge of  pump  per  stroke  was  measured  when  possible,  and  the 
diameter  of  cylinder  and  length  of  stroke  are  given,  so  that  the  dis- 
charge can  be  compared  with  the  figured  displacement.  The  lift  was 
measured  whenever  the  surface  of  the  water  in  the  well  could  be 
reached  with  a  tapeline.  The  number  of  strokes  of  the  pump  per 
mile  of  wind  was  found  for  velocities  from  6  or  8  miles  to  20  or  30 
miles  an  hour.  In  some  cases  the  number  of  strokes  is  given  when 
no  water  was  being  pumped.  In  fact,  there  was  collected  for  each 
mill  as  much  data  as  it  was  conveniently  possible  to  obtain  which 
would  in  any  way  affect  the  power  of  the  mill  or  be  of  interest. 

PUMPING  MILLS. 

The  essential  difference  between  pumping  and  power  mills  is  that 
in  the  former  there  is  a  pump  rod  with  an  up  and  down  motion,  while 
in  the  latter  there  is  a  vertical  rotating  shaft.  The  former  is  usually 
geared  back  2  or  3  to  1,  while  the  latter  is  generally  geared  forward 
6  or  8  to  1.  The  ordinary  pumping  mill,  such  as  is  used  for  stock 
purposes,  is  lighter  than  the  power  mill,  but  the  irrigating  mill  is  of 
nearly  the  same  weight  as  the  power  mill.  The  larger  power  mills 
have  a  pumping  attachment,  so  as  to  work  a  pump  as  well  as  a 
grinder  or  other  machine. 

WELLS   NEAR   GARDEN,    KANSAS. 

A  brief  description  of  the  water  supply  and  wells  of  this  locality 
may  be  helpful  in  considering  what  follows. 

The  water  is  found  in  sand  and  gravel  at  distances  below  the  sur- 
face varying  from  8  to  40  feet.  This  material  is  in  layers  of  variable 
thickness  and  different  degrees  of  coarseness,  ranging  from  fine  sand 


MURPHY.]  WRITER'S  EXPERIMENTS.  23 

to  large  gravel.  It  is  overlain  by  a  layer  of  sandy  clay,  which  in 
some  places  will  for  years  stand  vertical  without  any  support;  in 
other  places  there  is  very  little  clay  in  this  layer.  The  wells  are 
usually  3  to  4  feet  square,  and  are  cased  with  wood  through  the  top 
sandy  clay  to  the  water-bearing  sand;  then  a  wood  or  galvanized-iron 
casing  from  12  inches  to  3  feet  in  diameter  extends  down  from  8  to  20 
feet  into  the  sand  to  a  layer  of  gravel.  Where  this  latter  casing  is 
large,  three  or  more  galvanized-iron  pipes  6  to  12  inches  in  diameter 
are  put  down  in  the  bottom  of  it,  and  these  sometimes  have  wire 
gauze  over  their  tops  to  keep  down  the  sand ;  they  also  have  perfora- 
tions about  one-fourth  of  an  inch  in  diameter  for  a  distance  of  2  feet 
or  more  from  the  bottom  to  admit  the  water.  In  many  cases,  instead 
of  this  small  open  well,  the  supply  pipe  is  on  a  well  point  having  the 
same  diameter  as  the  supply  pipe,  its  length  varying  with  the  diame- 
ter. These  well  points  have  not  given  satisfaction  and  are  being 
replaced  b}7  open  wells. 

On  examining  well  points  that  have  been  used  for  a  time  it  was 
found  that  many  of  the  little  openings  through  which  water  is  admitted 
to  the  pump  had  become  filled  with  fine  grains  of  sand,  thus  reducing 
the  area.  Although  this  water  area  was  of  the  proper  amount  when 
the  well  was  new,  it  becomes  too  small  after  the  well  has  been  used 
for  a  time  or  after  it  has  stood  without  being  used.  If  this  area  is  too 
small  to  allow  the  free  passage  of  water  into  the  pump,  an  added 
load  is  put  on  the  latter. 

PUMPS. 

Nearly  all  of  the  pumps  in  use  in  the  vicinity  of  Garden  are  of  the 
reciprocating-piston  type.  Fig.  8  shows  the  Stone  pump,  manufac- 
tured by  R.  G.  Stone,  of  Garden.  This  pump  is  made  in  three  sizes — 
6  inch,  8  inch,  and  10  inch,  these  dimensions  being  the  approximate 
diameter  of  the  discharge  pipe.  The  diameter  of  the  cylinder  is  less 
than  the  diameter  of  the  pipe  by  twice  the  thickness  of  the  brass  lin- 
ing. The  valves  (shown  in  fig.  9)  are  of  the  latest  pattern.  The 
plunger  valve  is  of  the  single-fiap  or  clack  variety  and  the  check 
valvp  is  of  the  disc  variety,  made  so  that  the  water  can  pass  up  the 
center  as  well  as  around  the  sides.  In  an  earlier  form  of  this  pump 
the  plunger  valve  is  of  the  double-flap  or  butterfly  type  and  the  chock 
valve  of  the  lift  type,  but  with  no  opening  at  the  center.  Probably 
nine-tenths  of  the  pumps  in  use  near  Garden  are  of  the  Stone  variety. 

Fig.  3  shows  the  Gause  pump,  one  of  the  first  pumps  used  there  for 
irrigating  purposes.  It  is  more  expensive  than  the  Stone  pump,  and  is 
not  now  so  much  used.  Fig.  16  shows  the  cylinder  of  an  8-inch  Frizell 
pump,  a  few  of  which  are  in  use.  Fig.  5  is  a  sectional  view  of  the 
Woodmanse  pump,  which  is  used  with  mill  No.  2.  PI.  X,  B,  shows 
a  crude  homemade  pump  called  the  ' '  water  elevator. "  One  of  these 
is  in  use  in  Garden. 

The  efficiency  of  reciprocating  pumps  like  those  described  varies 


24 


THE    WINDMILL. 


[NO.  41. 


N 


directly  with  the  lift,  inversely  with  the  number  of  strokes  per  minute, 
and  with  the  design  of  the  pump.  For  lifts  of  10  or  more  feet  and  not 
more  than  30  strokes  per  minute  the  efficiency  in  a  good  pump  should 
be  at  least  70  per  cent. 

Prof.  O.  P.  Hood 1  has  measured  the  efficiency  of  two  Frizell  pumps — 
one  6  inch,  with  14.1  inches  stroke,  like  that 
shown  in  fig.  16,  and  one, ,4  inch,  with  24  inches 
stroke,  having  a  butterfly  discharge  valve.  He 
found  that  for  a  7.7-foot  lift  the  efficiency  of 
the  6-inch  pump  dropped  from  75  per  cent  to  63 
per  cent  as  the  number  of  strokes  increased 
from  10  to  60  per  minute;  that  for  a  22.7-foot  lift 
it  decreased  from  86  per  cent  to  82  per  cent  for 
the  same  range  of  speed;  and  that  for  a  37.8-foot 
lift  it  decreased  from  84  per  cent  to  82  per  cent, 
while  the  number  of  strokes  increased  from  10 
to  50  per  minute.  The  efficiency  of  the  4-inch 
pump  dropped  from  66  per  cent  to  60  per  cent 
for  a  12.8-foot  lift,  and  from  83  per  cent  to  73 
per  cent  for  a  37.6-foot  lift,  as  the  number  of 
strokes  increased  from  10  to  50  per  minute. 

The  valve  area  should  be  not  less  than  30  per 
cent  of  the  cylinder  area.  The  cylinder  should 
be  placed  as  near  the  water  as  possible;  if  it  is 
more  than  25  feet  above  the  water,  and  the 
number  of  strokes  is  30  or  more,  the  cylinder 
will  not  fill  properly,  and  pounding  will  result. 

INSTRUMENTS   AND   METHODS. 

The  wind  velocity  was  measured  with  a  United 
States  Weather  Bureau  cup  anemometer,  each 
mile  of  wind  being  recorded  electrically  b}^  one 
pen  of  a  2-pen  register.  By  means  of  a  little 
device  fastened  to  the  pump  an  electric  circuit 
is  closed  at  each  stroke  of  the  pump  and  a  record 
made  by  a  recorder.  Another  electric  circuit, 
leading  from  the  recorder  to  the  other  pen  of 
the  register,  is  closed  at  each  hundred  strokes 
of  the  pump  and  a  record  made  on  the  register. 
Hence  the  graphic  record  of  the  register  shows 
the  number  of  miles  of  wind  in  any  given  time,  also  the  number  of 
hundred  strokes  of  the  pump  in  the  same  time.  The  anemometer 
was  held  on  a  pole  at  the  height  of  the  axis  of  the  wheel  of  the  wind- 
mill. The  pole  was  made  so  that  its  length  could  be  increased  at 
will  from  25  to  50  feet.  The  anemometer  on  the  pole  is  shown  in  Pis. 
Ill  and  XI. 


S 


FIG.  3.— Gause  pump.  JV, 
plunger;  B,  spout;  F,  dis- 
charge pipe;  H,  plunger; 
T,  cylinder;  Z,  enlarged 
valve  opening  and  check 
valve;  S,  suction  pipe. 


1  Water-Supply  and  Irrigation  Paper  U.  S.  Geol.  Survey  No.  14. 


MURPHY.]  WRITER'S  EXPERIMENTS.  25 

The  discharge  of  the  pump  per  stroke  was  ascertained  by  catching 
the  water  for  several  strokes  in  a  tub  and  measuring  it  with  a  quart 
measure.  In  a  few  cases  it  was  found  to  vary  with  the  number  of 
strokes  per  minute.  Where  it  varied  the  discharge  given  is  for  a 
nearly  maximum  speed  of  pump. 

The  lift,  or  distance  from  the  surface  of  the  water  in  the  well 
to  the  center  of  the  -~ ater  column  as  it  leaves  the  discharge  pipe, 
was  measured  when  the  pump  was  working  quite  rapidly.  For 
pumps  on  well  points  it  was  estimated  from  the  depth  to  water  when 
the  point  was  put  down,  making  an  allowance  for  the  lowering  of 
the  water. 

Each  mill  tested  is  described  and  the  results  of  the  tests  given  in 
tabular  form.  Nearly  all  of  the  mills  are  illustrated. 

The  number  of  strokes  of  the  pumps  per  mile  of  wind  and  the  horse- 
powers of  the  mills  are  in  most  cases  explained  by  diagrams,  which 
show  at  a  glance  the  facts  which  otherwise  can  be  comprehended  only 
by  a  careful  analysis  of  the  tables.  In  these  diagrams  (figs.  6,  10,  11, 
12,  13,  15,  17,  18,  19,  and  21)  the  relation  between  the  wind  move- 
ment, in  miles  per  hour,  and  the  number  of  strokes  made  by  the 
pump  while  the  wind  was  moving  over  1  mile  is  shown  by  the  curved 
line.  The  space  from  left  to  right  is  proportional  to  the  number 
of  strokes  of  the  pump.  The  data  expressed  by  these  diagrams 
were  obtained  directly  from  the  record  given  by  the  anemometer 
register. 

In  explanation  we  will  assume  that  the  pen  connected  with  the 
anemometer  makes  three  short  marks  (3  miles)  in  fifteen  minutes, 
indicating  a  mile  in  five  minutes,  or  at  the  rate  of  12  miles  an  hour. 
At  the  same  time  the  other  pen  connected  with  the  pump,  and  regis- 
tering each  100  strokes,  makes,  saj7,  two  short  marks,  showing  that 
the  pump  has  made  200  strokes  for  this  3  miles  of  wind  movement, 
or  67  strokes  to  the  mile.  This  fact  is  entered  on  the  diagram  by 
a  small  circle  placed  at  a  distance  from  the  right  which  corre- 
sponds to  a  wind  velocity  of  12  miles  an  hour,  and  at  a  distance  from 
the  bottom  which  corresponds  to  67  strokes  of  the  pump.  In  this  way 
each  observation  is  indicated.  When  the  points  have  been  plotted, 
the  smooth  curve  is  sketched  so  as  to  occupy  an  intermediate  position 
among  them. 

In  order  to  obtain  the  number  of  strokes  more  accurately  than  by 
measurement  on  the  register  sheet,  they  were  actually  counted  for 
a  considerable  number  of  observations  in  each  test.  The  number  of 
strokes  per  minute  is  obtained  by  dividing  the  number  of  strokes  per 
mile  of  wind  by  the  number  of  minutes  required  to  make  the  mile. 
For  example:  If  the  number  of  strokes  per  mile  in  a  12-mile  wind 
(which  requires  60  -4-  12,  or  five  minutes  to  make  a  mile)  is  90,  then 
90  -r-  5  =  18,  the  number  of  strokes  per  minute.  The  number  of  gal- 
lons raised  per  minute  is  found  by  multiplying  the  number  of  gallons 


26  THE    WINDMILL. 


[NO.  41. 


per  stroke  by  the  number  of  strokes  per  minute.     The  horsepower  of 
the  mill  in  any  wind  velocity  is  found  by  multiplying  the  number  of 


Ki<;.  4.— Working  parts  of  Woodmanse  Mogul. 

per  stroke  by  UK*  number  of  strokes  per  minute,  then  by  8.3 
pounds  (the  weight  of  one  Ballon   of  water),  then  by  the  lift,  in  feet, 


MURPHY.] 


PUMPING    MILLS    TESTED. 


27 


and  dividing  the  product  by  33,000  (the  number  of  foot-pounds  in  a 
horsepower),  or  by  the  following  formula: 

Horsepower  =  nqgh  -+-  33,000,  where  n  —  number  of  strokes  per 
minute,  g  =  the  weight  of 
one  gallon  of  water,  q  =  the 
number  of  gallons  per  stroke 
of  pump,  h  =  the  lift,  in  feet. 
The  pump  load  is  the  weight 
of  water  lifted  per  stroke 
multiplied  by  the  lift,  or 
height  to  which  it  is  raised. 
The  number  of  revolutions 
of  the  wind  wheel  per  minute 
is  found  by  multiplying  the 
number  of  strokes  per  min- 
ute by  the  number  of  revolu- 
tions per  stroke. 

PUMPING   MILLS   TESTED. 

Mill  No.  1.—  The  tests  of 
this  mill  were  preliminary 
or  experimental,  being  made 
for  the  purpose  of  perfecting 
the  instruments  employed, 
and  were  not  completed  for 
discussion. 

Mill  No.  '2.  —This  is  a 
12-foot  Woodmanse  Mogul, 
manufactured  by  the  Wood- 
manse-Hewitt  Manufactur- 
ing Company,  of  Freeport, 
Illinois.  PI.  Ill  shows  the 
mill,  tower,  pump,  and  pond, 
and  fig.  4  the  working  parts. 
The  tower  is  of  steel,  50  feet 
high  to  the  axis  of  the  wheel. 
The  wind  exposure  on  the 
north,  is  not  good,  the  mill 
being  115  feet  south  of  a 
large  barn.  The  wheel  has 
30  curved  sails,  each  36  by  13 
by  5.5  inches,1  set  at  an  angle 
of  30°  (angle  of  weather)  with 
the  plane  of  the  wheel.  It  is 
back- geared,  3  to  1,  and  held  in  the  wind  by  a  spring. 


FIG.  ").— Sectional  view  of  Woodmanse  pump. 


The  pump 


1  In  this  expression  36  is  the  length  of  the  sail,  13  the  width  of  sail  at  the  outer  end,  and  5.5 
the  width  of  sail  at  the  inner  end. 


28 


THE    WINDMILL. 


[NO.  41. 


also  is  of  Woodmanse  make,  and  is  shown,  in  section,  in  fig.  5.  The 
cylinder  is  9.5  inches  in  diameter,  the  supply  pipe  5.625  inches  in 
diameter,  the  length  of  stroke  12  inches.  The  well  is  3f  feet  by 
3f  feet  to  the  water,  a  distance  of  14  feet.  At  that  point  a  12-inch 
galvanized-iron  pipe  is  put  down  20  feet,  forming  a  small  open  well. 
The  lift  at  the  time  of  test  was  17f  feet  and  the  discharge  per  stroke 
14|  quarts.  The  mean  barometric  pressure  was  26.98  inches,  and  the 
mean  temperature  94°  F.  The  cost  of  mill,  tower,  pump,  and  well 
was  about  $210.  The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  2— 12-foot  Woodmanse  Mogul. 
[Load  per  stroke,  536.2  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

U 

hnrs 

12  miles 

15.6 

5  2 

18  8 

16  miles 

48.0 

16.0 

58  0 

20  miles 

60.9 

20.3 

73.6 

25  miles 

69.9 

23.3 

84.5 

30  miles  

75.9 

25.3 

91.7 

Useful 


0.  085 
0.260 
0.  322 
0.  379 
0.  41 1 


The  curve  shown  in  fig.  6  is  for  a  moderately  loaded  12-foot  mill 
(536.2  foot-pounds  per  stroke).     It  starts  at  a  wind  velocity  of  11 


10 


VELOCITY  OP  WIND  IN  MILES  PER  HOUR, 

15  20  25 


70 


FIG.  ti. — Diagram  showing  results  with  mill  No.  2 — 12-foot  Woodnuuiso  Mogul. 


U.   S.    GEOLOGICAL  SURVE1 


WATER-SUPPLY   PAPER   NO.    41       PL.    Ill 


VIEW   OF    MILL   NO.  2   (12-FOOT  WOODMANSE   MOGUL)   AND   ANEMOMETER. 


MURPHY.] 


PUMPING    MILLS    TESTED. 


29 


miles  an  hour.  It  ascends  very  rapidly,  reaching  a  maximum  at  18 
miles  an  hour,  and  giving  60  strokes  to  the  mile.  The  rest  of  the 
curve  to  30  miles  has  a  gentle  slope.  The  number  of  strokes  per 
minute  increases  from  about  5  at  12  miles  to  about  25  at  30  miles  an 
hour,  and  will  continue 
to  increase  to  probably 
28  a  minute  in  a  40-mile 
wind. 

Mill  No.  3.—  This  is  a 
12-foot  Aermotor  manu- 
factured by  the  Aermotor 
Company,  of  Chicago, 
Illinois.  PI.  IV  shows 
the  mill  with  its  tower, 
pump,  and  pond,  and  fig. 
7  shows  its  working 
parts.  This  mill  had  been 
in  use  about  one  year  at 
the  time  of  test,  and  all 
of  the  parts  were  in  good 
working  order.  The 
tower  is  of  wood,  the  axis 
of  the  wheel  being  30  feet 
above  the  ground.  The 
exposure  is  very  good. 
The  wheel  has  18  curved 
sails,  each  44  by  18f  by  7| 
inches,  set  at  an  angle  of 
31°  to  the  plane  of  the 
wheel.  It  is  back-geared, 
3^  to  1,  and  is  held  in  the 
wind  by  a  spring.  The 
pump  is  of  the  Stone  type, 
shown  in  figs.  8  and  9; 
the  check  valve  is  of  the 
single-flap  variety,  the 
plunger  valve  of  the 
double-flap  variety.  The 
cylinder  is  9£  inches  in 

diameter,  the  supply  pipe  4  inches  in  diameter,  and  the  discharge 
pipe  10  inches  in  outside  diameter;  the  length  of  stroke  is  12  inches 
and  the  discharge  per  stroke  14-J  quarts.  The  well  is  4  feet  by  4 
feet  to  a  depth  of  8  feet — nearly  down  to  water.  From  that  point 
to  a  depth  of  18  feet  it  is  3  feet  in  diameter;  and  from  there 
three  pipes,  12  inches  in  diameter,  extend  down  5  feet  farther.  The 
lift  at  the  time  of  test  was  13|  feet,  the  barometric  pressure  27.2 
inches,  and  the  temperature  85°  F.  The  water  is  pumped  into  a  pond 


FIG.  7.— Working  parts  of  Aermotor 


30 


THE    WINDMILL. 


[NO.  41. 


80  feet  by  75  feet,  and  a  depth  of  22  inches  can  be  drawn  off.  The 
cost  of  the  plant,  including  mill,  tower,  pump,  and  pond,  was  $145. 
The  greatest  number  of  strokes  per  minute  is  probably  27  or  28  in  a 
40-mile  wind.  In  general  appearance  this  curve  is 
seen  to  resemble  that  of  mill  No.  2,  but  it  is  about 
4  miles  farther  to  the  left,  due  to  lighter  load. 
The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mitt  No.  3— 12-foot  Aermotor. 
[Load  per  stroke,  415.3  foot-pounds.] 


Wind  velocity  per 
hour. 

Revolu- 
tions of 
wind  wheel 
per  minute. 

Strokes  of 
pump 
per  minute. 

Gallons 
pompedper 

minute. 

Useful 
horse 
power. 

8  miles  

17.7 

5.3 

19.3 

0  067 

12  miles  
16  miles 

40.0 
54.7 

12.0 
16.4 

43.5 
59  5 

0.  151 

0  207 

20  miles  
25  miles  ..   ... 
30  miles  .  

66.0 

77.0 
83.3 

19.8 
23.1 
25.0 

71.8 
83.6 
90.6 

0.  250 
0.291 
0.315 

The  curve  shown  in  fig.  10  is  for  a  rather 
lightly  loaded  mill  (415.3  foot-pounds  per  stroke). 
It  starts  at  a  velocity  of  6  to  7  miles  an  hour, 
ascends  less  rapidly  than  the  one  shown  in  fig.  6, 
attains  a  maximum  at  about  15  miles  an  hour, 
when  the  number  of  strokes  per  mile  is  62,  and 
then  descends  slowly,  reaching  50  strokes  at  30 
miles.  The  number  of  strokes  per  minute  increases 
from  about  5  at  8  miles  to  25  at  30  miles. 

Mill  No.  4- — This  mill,  shown  in  the  foreground 
of  PI.  V,  is  an  8-foot  Ideal  windmill  manufactured 
by  the  Stover  .Manufacturing  Company,  of  Free- 
port,  Illinois.  It  had  been  in  use  about  one  year, 
and  all  of  the  parts  were  in  good  condition.  The 
tower  is  of  wood,  the  axis  of  the  wheel  being  48  feet  above  the  ground. 
The  wheel  has  15  sails,  each  16^  by  7  by  30  inches,  set  at  an  angle 
of  29°  with  the  plane  of  the  wheel.  It  is  back-geared,  2|  to  1,  and  is 
held  in  the  wind  by  a  spring.  The  pump  is  of  the  Stone  make.  The 
diameter  of  the  discharge  pipe  is  5f  inches,  of  the  supply  pipe  3  inches. 
The  length  of  stroke  is  8  inches.  The  plunger  and  check  valves  are 
of  the  single-flap  variety.  The  \\ell  is  2f  feet  by  2|  feet  down  nearly 
to  water— a  depth  of  5£  feet.  The  o-inch  supply  pipe  extends  down 
to  a  depth  of  1  1  feet,  and  on  the  end  of  it  is  a  3-ineh  well  point  6  feet 
long.  The  lift  may  vary  from  s.l  to  20  foot.  It  \vas  probably  about 
12  feet  at  the  time  of  tests.  The  discharge  per  stroke  was  2  quarts. 
The  mean  barometric  pressure  was  ^7.1!)  inches,  the  mean  tempera- 


FIG.  8.— Stone  pump. 


MURPHY.] 


PUMPING    MILLS    TESTED. 


31 


tare  83°  F.  The  water  is  pumped  into  a  pond  115  feet  by  31  feet  and 
3  feet  deep.  The  cost  of  the  plant,  including  mill,  pump,  well,  and 
pond,  was  $80.  The  results  of  the'tests  are  as  follows: 

Results  of  tests  of  mill  No.  4 — 8-foot  Ideal. 
[Load  per  stroke,  50  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
Dump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles 

25.5' 

10.2 

5.1 

0.015 

16  miles 

48.2 

19.3 

9.6 

0.029 

20  ini!es      -   

63.2 

25.3 

12.6 

0.038 

25  miles 

70.3 

28.1 

14.1 

0.043 

30  miles        -  -  .  .  

62.5 

25.0 

12.5 

0.038 

FK;.  '.). —Details  of  Stone  pump:  a,  Lower  valve  seat;  6,  ring  guide  to  lower  valve;  c,  lower  or 
check  valve;  d,  hook  for  removing  lower  valve;  e,  plunger  and  valve;  /  is  a,  6,  and  c  com- 
bined. 

The  curve  shown  in  fig.  11,  although  for  a  rather  lightly  loaded 
mill— 50  foot-pounds  per  stroke — shows  that  the  mill  starts  in  a  10- 
mile  to  an  11-mile  wind.  The  maximum  is  reached  at  19  miles,  with 
a  speed  of  78  strokes.  The  right  side  of  the  curve  is  quite  steep,  a 
characteristic  of  this  make  of  mill.  Mill  No.  18  is  the  same  size  and 
make  as  this  mill,  and  yet  with  a  load  of  89.2  foot-pounds  it  starts  in 
a  7-mile  to  an  8-mile  wind,  reaching  a  maximum  at  about  13  miles,  at 


32 


THE    WINDMILL. 


[NO.  41. 


10 


VELOCITY  OP  WIND  IN  MILES  PER  HOUR. 
0 


70 


fid 


50 


40 


20 


10 


FIG.  10.— Diagram  showing  results  with  mill  No.  3— 12-foot  Aeruaotor. 


10 


VELOCITY  OP   WIND   IN  MILES  PER  HOUR. 
15  20 


o  o 


H5 


£50 


°1 


40 


FIG.  11.— Diagram  showing  results  with  mill  No.  4— 8-foot  Ideal. 


MURPHY.] 


PUMPING    MILLS    TESTED. 


33 


a  speed  of  104  strokes  per  mile.  A  second  test,  when  the  spring  that 
holds  the  wind  wheel  in  the  wind  was  tightened  somewhat,  gave  the 
maximum  at  a  velocity  of  about  15  miles,  with  a  pump  speed  of  about 
114  strokes.  The  difference  appeared  to  be  due  to  the  difference  in 
pumps  and  wells.  The  rapid  fall  in  the  curve  to  the  right  of  the  high- 
est point  is  due  to  the  easy  governing  of  the  mill. 

Mill  No.  5. — This  mill,  shown  in  the  background  of  PI.  V,  is  an 
8-foot  Aermotor  manufactured  by  the  Aerinotor  Company,  of  Chicago, 
Illinois.  The  tower  is  of  wood,  and  is  28. 5  feet  high  to  the  axis  of  wheel. 
The  exposure  is  good,  and  all  of  the  parts  were  in  good  working  order 
at  the  time  of  tests,  the  plant  having  been  in  use  about  one  year.  The 
wheel  has  18  curved  sails,  each  30  by  12-j-  by  o^  inches,  making  an 
angle  of  29-j-0  with  the  plane  of  the  wheel.  It  is  back-geared,  3£  to  1. 
The  pump  is  of  the  Stone  make.  The  discharge  pipe  is  6  inches  in 
diameter,  the  supply  pipe  3  inches  in  diameter.  The  valves  (check 
and  plunger)  are  of  the  single-flap  variety.  The  length  of  stroke  is 
8  inches.  The  well  is  4  feet  by  4  feet  to  water,  a  depth  of  10. 5  feet. 
A  12-inch  wooden  curb  extends  12  feet  farther  into  the  sand  and 
gravel.  The  discharge  per  stroke  was  3^  quarts,  and  the  lift  13  feet. 
The  cost  of  plant,  including  pond,  was  $80. 


VELOCITY  OP  WIND  IN  MILES  PER  HOUR. 
10  15  20  35 


ICO 


70 


a  i 


40 


FIG.  12. — Diagram  showing  results  with  mill  No.  5 — 8-foot  Aermotor. 
IRR  41 — 01 8 


34  THE    WINDMILL. 

The  results  of  the  tests  of  mill  No.  5  are  as  follows: 

Results  of  tests  of  mill  No.  5 — 8-foot  Aermotor. 
[Load  per  stroke,  94.9  foot-pounds.] 


[NO.  41. 


"Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles 

62.0 

18.6 

16  3 

0  053 

16  miles            

83.7 

25.1 

22.0 

0  072 

20  miles  

99.3 

29.8 

26.1 

0.086 

25  Tnilfis 

115.3 

34.6 

30  3 

0  099 

30  miles 

128.3 

38.5 

33.7 

0  111 

This  8-foot  mill,  with  a  load  of  95  foot-pounds,  is  seen  to  start  in 
an  8-mile  to  a  9-mile  wind  (fig.  12),  reaching  a  maximum  at  13  to  15 
miles,  with  95  strokes  per  mile.  At  30  miles  an  hour  it  is  making  77 
strokes  per  mile,  or  39  strokes  per  minute.  This  curve  indicates  a 
rather  heavily  loaded  mill. 

Mill  No.  6. — This  mill,  shown  in  the  background  of  PI.  IV,  is  an 
8-foot  Gem,  manufactured  by  the  United  States  Wind  Engine  and  Pump 
Company,  of  Kansas  City,  Missouri.  The  working  parts  of  the  mill 
are  shown  in  PI.  VI.  The  exposure  was  good  and  all  of  the  parts  were 
in  good  working  order,  the  mill  having  been  in  use  only  about  one 
year  at  the  time  of  tests.  The  wheel  has  24  curved  sails,  each  30|  by 
10  by  4£  inches,  set  at  an  angle  of  35°  with  the  plane  of  the  wheel.  It 
is  back-geared,  3  to  1.  The  wheel  is  held  in  the  wind  by  means  of  a 
weight.  The  pump  is  of  the  Stone  make.  The  discharge  pipe  is  6 
inches  in  diameter,  the  supply  pipe  4  inches  in  diameter.  The  length 
of  stroke  is  8  inches.  The  well  is  open  to  the  water — a  depth  of  6-J 
feet.  The  supply  pipe  is  on  a  well  point,  the  end  of  which  is  Ifi  feet 
below  the  surface  of  the  ground.  The  lift  was  9T^  feet  and  the  dis- 
charge per  stroke  3.9  quarts.  The  tower  is  of  wood,  and  is  24  feet 
high  to  the  axis  of  the  wheel.  The  mean  barometric  pressure  was  27.02 
inches,  the  mean  temperature  85°  F.  The  plunger  valve  is  of  the 
double-flap  variety,  and  the  check  valve  of  the  single-flap  variety. 
The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  c, — 8-foot  Gem. 

[Load  per  stroke,  77.6  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

12  miles 

37.2 

12.4 

16  miles        

.•»:',.  7 

17.9 

20  miles  

86.0 

22.0 

25  miles 

76.2 

25.4 

30  miles 

85.  5 

28.  5 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12.  1                0.  029 

17.5              0.0-12 

21.5              0.051 

24.  7               0.  059 

27.8 

0.065 

MURPHY.] 


PUMPING    MILLS    TESTED. 


35 


Comparing  the  number  of  strokes  per  minute  of  mills  Nos.  4,  5,  and 
6,  it  is  seen  that  although  No.  5  is  carrying  a  much  heavier  load  than 
either  of  the  other  mills,  it  makes  more  strokes  and  does  much  more 
work  at  all  velocities. 

Mill  No.  7.— This  is  a  12-foot  Aermotor  similar  to  mill  No.  3.  The 
tower  is  of  steel,  having  a  height  of  31  feet  to  the  axis  of  the  wheel. 
The  exposure  was  good  and  all  of  the  parts  were  in  good  working  order, 
the  plant  having  been  in  use  less  than  one  year  when  tests  were  made. 
The  pump  is  of  the  Stone  make  and  is  like  that  of  mill  No.  3,  except 
that  the  check  valve  is  of  the  solid-lift  variety.  The  lift  was  15-J-  feet 
and  the  discharge  14.3  quarts  per  stroke.  The  water  is  pumped  into 
a  pond  135  feet  by  50  feet  by  2|  feet. 

Comparing  the  results  of  the  tests  of  this  mill  with  those  of  mill 
No.  3,  it  is  seen  that  the  latter  is  somewhat  more  heavily  loaded  than 
the  former  and  makes  a  few  less  strokes  per  minute,  but  that  its 
horsepower  is  a  little  greater.  The  effect  of  the  larger  load  is  shown. 

The  results  of  the  tests  of  mill  No.  7  are  as  follows: 

Results  of  tests  of  mill  No.  7— 12-foot  Aermgtoj\ 
[Load  per  stroke,  461.9  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
puinp  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles               

38.0 

11.4 

40.7 

0.160 

16  miles 

52.7 

15.8 

56.5 

0.221 

20  miles 

63.3 

19.0 

67.9 

0.266 

25  miles  . 

73.7 

22.1 

79.0 

0.309 

30  miles 

78.3 

23.5 

84.0 

0.329 

Mill  No.  8. — This  is  a  10- foot  Star  wooden  mill,  manufactured  by 
Bradley,  Wheeler  &  Company,  of  Kansas  City,  Missouri.  The  tower 
is  of  wood,  and  the  axis  of  the  wheel  35|  feet  above  the  ground.  The 
water  is  pumped  into  an  elevated  tank  20  feet  above  the  surface  of 
the  ground  and  is  used  for  irrigation.  The  wheel  has  60  plane  sails, 
each  37  by  5  by  2f  inches,  set  at  an  angle  of  33°  to  the  plane  of  the 
wheel.  It  is  held  in  the  wind  by  means  of  a  weight.  It  is  not  back- 
geared,  a  stroke  of  the  pump  being  made  to  each  revolution  of  the 
wheel.  The  supply  pipe  is  2  inches  in  diameter  and  terminates  in  a 
well  point,  the  end  of  which  is  18  feet  below  the  surface  of  the  ground. 
The  discharge  pipe  is  1£  inches  in  diameter.  The  cylinder  is  3  inches 
in  diameter,  the  length  of  stroke  5  inches.  The  lift  may  vary  between 
28-J-  and  37  feet.  It  was  estimated  to  be  about  30  feet  at  the  time  of 
measurement.  The  discharge  per  stroke  was  0.24  quart.  The  cylin- 
der leaked  some  at  the  time  of  tests.  After  a  new  cylinder  was  put 
in  the  discharge  per  stroke  was  increased  to  0.40  quart.  The  mean 


36 


THE    WINDMILL. 


[NO.  41. 


barometric  pressure  was  27.04  inches,  the  mean  temperature  78°  F. 
The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  8— 10-foot  Star  icooden  mill. 
[Load  per  stroke,  15  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

28.0 

28.0 

1.7 

0.013 

12  miles      ... 

30.0 

30.0 

1.8 

0.014 

These  results  show  the  effect  of  the  very  light  load  and  the  readi- 
ness with  which  the  wind  wheel  turns  out  of  the  wind.  It  makes  28 
strokes  per  minute  in  an  8-mile  wind  and  less  than  that  in  a  16-mile 
or  higher  wind. 

Mill  No.  9. — This  is  a  16-foot  Aermotor.  The  tower  is  of  steel,  and 
the  axis  of  the  wheel  is  30  feet  above  the  ground.  The  wheel  has  18 


10 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

15  30  25 


80 


till 


.  40 


Fio.  13.— Diagram  showing  results  with  mill  No.  9— Itt-foot  Aermotor. 

curved  sails,  each  59  by  25|  by  10J  inches,  set  at  an  angle  of  30°  with 
the  plane  of  the  wheel.  It  is  back-geared,  3  to  1.  The  discharge 
pipe  is  12  inches  in  diameter,  the  supply  pipe  6  inches  in  diameter, 
the  cylinder  8  inches  in  diameter.  The  stroke  is  1 6  inches.  The  well 
is  4  feet  by  6  feet  to  a  depth  of  23  feet,  2  feet  by  2  feet  for  the  next  8 
feet,  and  1 8  inches  in  diameter  for  the  next  14  feet.  The  water  was  39£ 
feet  below  the  surface  of  the  ground. .  The  lift  was  44J  feet  and  the 


MURPHY.] 


PUMPING    MILLS    TESTED. 


37 


discharge  per  stroke  11  quarts.  The  check  valve  is  of  the  single-flap 
variety  and  the  plunger  valve  of  the  double-flap  variety.  The  mean 
barometric  pressure  was  27.04  inches,  and  the  mean  temperature  93° 
F.  This  plant  had  been  in  use  about  three  years.  The  results  of  the 
tests  are  as  follows: 

Results  of  tests  of  mitt  No.  9— 16-foot  Aermotor. 
[Load  per  stroke,  1,013  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles 

31.8 

10.6 

29.1 

0.325 

16  miles    

42.3 

14.1 

38.8 

0.433 

20  miles  

51.6 

17.2 

47.3 

0.548 

25  miles 

58.8 

19.6 

53.9 

0.601 

30  miles  

63.0 

21.0 

57.7 

0.644 

The  curve  shown  in  fig.  13  starts  at  a  wind  velocity  of  8  to  9  miles, 
and  reaches  a  maximum  at  13  miles,  with  a  speed  of  53  strokes  per 
mile.  From  that  point  to  a  velocity  of  about  19  miles  the  curve  is 
nearly  horizontal;  after  19  miles  it  descends  slowly  to  32  miles,  with 
38  strokes  per  mile.  The  speed  increases  from  11  strokes  per  minute 
at  12  miles  to  21  strokes  per  minute  at  30  miles  an  hour. 

Mill  No.  10. — This  is  an  8-foot  Ideal.  The  tower  is  of  wood,  the 
axis  of  the  wheel  being  30  feet  above  the  ground.  The  wheel  has  15 
curved  sails,  each  31  by  19  by  7  inches,  set  at  an  angle  of  29-J-0  with 
the  plane  of  the  wheel.  It  is  back-geared,  2-j-  to  1.  The  supply  pipe- 
is  1-j-  inches  in  diameter,  the  cylinder  2-J-  inches  in  diameter.  The 
pump  is  a  common  hand  pump,  with  lift  valve  of  the  flap  form  and 
plunger  of  the  lift  variety.  The  valves  leak  some,  as  the  discharge  is 
greater  when  the  pump  is  working  rapidly  than  when  it  is  working 
slowly.  The  supply  pipe  is  on  a  well  point  2  feet  long  and  1-J  inches 
in  diameter,  the  lower  end  of  which  .is  50  feet  below  the  surface  of  the 
ground.  The  lift  was  33  feet  and  the  discharge  per  stroke  one-third 
of  a  quart  when  pumping  quite  rapidly.  The  mean  barometric  pres- 
sure was  26. 94  inches,  the  mean  temperature  97°  F.  The  results  of  the 
tests  are  as  follows: 

Results  of  tests  of  mitt  No.  10 — 8-foot  Ideal. 
[Load  per  stroke,  22. 8  foot-pounds.  ] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles  

35  2 

14  1 

1  2 

0  010 

12  miles 

62  5 

25  0 

2  1 

0017 

16  miles  

83  2 

33  3 

2  8 

0  0°3 

20  miles  

0  032 

38 


THE    WINDMILL. 


[NO.  41. 


Mill  No.  11. — This  is  a  12-foot  Ideal,  the  working  parts  of  which 
are  shown  in  fig.  14.  The  tower  is  of  steel,  the  axis  of  the  wheel 
being  30  feet  above  the  ground.  The  exposure  was  good,  and  all  of  the 


FIG.  14.— Working  parts  of  mill  No.  11— 13-foot  Ideal. 

parts  were  in  good  working  order  when  mill  was  tested.  The  wheel 
has  21  curved  sails,  each  31  by  19  by  7  inches,  set  at  an  angle  of  29|° 
to  the  piano  of  t.h<>  wheel.  II  is  b;i<-k-i»vaivd,  24  to  1,  and  the  wheel 


MURPHY.] 


PUMPING    MILLS    TESTED. 


39 


is  held  in  the  wind  by  a  spring.  The  discharge  pipe  is  8  inches  in 
diameter,  and  the  length  of  stroke  is  12  inches.  The  supply  pipe 
consists  of  two  3-inch  pipes  14  feet  long,  each  terminating  in  a  3-inch 
well  point  3  feet  long.  The  valves  (check  and  plunger)  are  of  the 
single-flap  variety.  The  water  was  39  feet  below  the  surface  of  the 
ground.  The  lift,  as  nearly  as  could  be  ascertained  at  the  time  of 
measurement,  was  45  feet,  the  discharge  per  stroke  9  quarts.  The 
water  is  pumped  into  a  pond  60  feet  by  40  feet  by  6  feet.  This  plant 
had  been  in  use  about  three  years.  The  mean  barometric  pressure 
was  26.91  inches,  the  mean  temperature  91°  F.  The  results  of  the 
tests  are  as  follows : 

Results  of  tests  of  mill  No.  11— 12-foot  Ideal. 
[Load  per  stroke,  843.7  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles        

12.0 

4.8 

10.8 

0.123 

16  miles 

31.7 

12.7 

28.6 

0.325 

20  miles            .  - 

47.0 

18.8 

42.3 

0.481 

25  miles          .         

58.2 

23.3 

52.5 

0.600 

30  miles 

62.5 

25.0 

56.2 

0.639 

Mills  Nos.  9  and  11  pump  water  into  the  same  pond  from  the  same 
depth.     It  will  be  seen  from  these  results  that  for  wind  velocities  of 


10 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

15  30  25 


40 


30 


10 


FIG.  15.— Diagram  showing  results  with  mill  No.  11— 13-foot  Ideal. 


40 


THE    WINDMILL. 


[NO.  41. 


20  miles  or  more  the  12-foot  mill  is  pumping  nearly  as  much  water  as 
the  16-foot  mill;  for  velocities  of  12  miles  or  less  the  16-foot  mill  is 

pumping  much  more  water  than 
the  12-foot  mill. 

This  curve  (fig.  15)  is  for  a 
heavily  loaded  (843.7  foot- 
pounds per  stroke)  12-foot  mill. 
It  starts  with  a  velocity  of  about 
10  miles  an  hour,  and  reaches 
a  maximum  at  about  23  miles, 
with  a  speed  of  57  strokes  per 
mile.  At  30  miles  it  is  making 
51  strokes  per  mile.  The  maxi- 
mum point  of  this  curve  is  much 
farther  to  the  right  than  that  of 
any  other  curve.  The  number 
of  strokes  increases  from  5  per 
minute  at  12  miles  to  25  per 
minute  at  30  miles. 

Mitt  No.  12.—  This  is  a  14-foot 
Ideal,  shown  in  PL  VII.  The 
tower  is  of  steel  and  is  30  feet 
high  to  the  axis  of  the  wheel. 
The  wheel  has  24  curved  sails, 
each  48f  by  17-J-  by  8  inches,  set 
at  an  angle  of  30°  with  the  plane 
of  the  wheel.  It  is  back-geared, 
2-J-  to  1.  The  pump  is  of  the 
Frizell  make  (shown  in  fig.  16). 
The  discharge  pipe  is  10  inches 
in  diameter,  the  cylinder  9| 
inches  in  diameter,  the  supply 
pipe  6  inches  in  diameter,  ter- 
minating in  a  well  point  10  feet 
long  and  6  inches  in  diameter, 
the  lower  end  of  which  is  32  feet 
below  the  surface  of  the  ground. 
The  lift,  as  nearly  as  could  be 
estimated,  was  11  fed,  the  dis- 
charge per  stroke  11.  (J  quarts. 
The  mean  barometric  pressure 
was  27.04  indies,  the  mean  tern- 

FK,ir,-Working  parts  of  Prize.,  cyHnder.  I"'' •>< '"'<'    *1"    *'•       The   Water    U 

pumped  into  a  reservoir  KM)  feet 

by  100  feet  by  3  feet  deep.     The  pump  had   been   in  use  about  one 
year.     The  results  of  the  tests  are  as  follows: 


U.    S.    GEOLOGICAL  SURVEY 


WATER-SUPPLY  PAPER  NO.   41       PL.   VI 


WORKING    PARTS  OF   MILL   NO.  6— 8-FOOT  GEM. 


MURPHY.] 


PUMPING    MILLS    TESTED. 


41 


Results  of  tests  of  mill  No.  12— 14-foot  Ideal. 
[Load  per  stroke,  363.5  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

7.7 

3.1 

8.9 

0.025 

12  miles                     

27.2 

10.9 

30.1 

0.087 

16  miles 

39.3 

15.7 

45.1 

0.125 

20  miles 

48.0 

19.2 

55.2 

0.153 

25  miles           .     ..... 

53.7 

21.5 

61.8 

0.173 

This  curve  (fig.  17)  is  for  a  very  lightly  loaded  (263.5  foot-pounds) 
14-foot  mill.  This  load  is  only  31  per  cent  of  that  of  the  12-foot  mill, 
No.  11.  The  curve  starts  in  a  7-mile  to  an  8-mile  wind,  and  reaches 
a  maximum  at  15  miles,  with  a  speed  of  58  strokes  per  mile  of  wind. 
At  30  miles  the  speed  is  47  strokes.  Although  this  is  a  very  lightly 


10 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

15  30 


60 


1C 


FIG.  1?.— Diagram  showing  results  with  mill  No.  13— 14-foot  Ideal. 

loaded  mill  it  does  not  make  many  strokes  per  minute.  In  fact, 
although  it  is  not  as  heavily  loaded  as  the  12-foot  mill,  No.  3,  it  does 
not  make  as  many  strokes  per  minute  as  the  latter  mill,  and  it  is  pro- 
ducing much  less  power  than  mill  No.  3. 

Mitt  No.  13.—  This  is  a  12-foot  Aermotor  (shown  in  PL  VIII).  The 
tower  is  of  wood,  with  the  axis  of  the  wheel  25  feet  above  the  ground. 
The  exposure  was  good  and  the  plant  in  excellent  condition,  having 


42 


THE    WINDMILL. 


[NO.  41. 


been  in  use  about  one  year  at  the  time  of  tests.  The  wheel  is  the  same 
as  that  of  No.  3.  The  pump  is  of  the  Stone  make.  The  discharge  pipe 
is  10  inches  in  diameter,  the  supply  pipe  5  inches  in  diameter,  on  a 
well  point  10  feet  long,  the  lower  end  of  which  is  17  feet  below  the 
surface  of  the  ground.  The  length  of  stroke  is  12  inches.  The 
plunger  valve  is  of  the  double-flap  type,  and  the  check  valve  of  the 
single-flap  type.  The  discharge  per  stroke  at  the  time  of  test  was 
14.4  quarts  and  the  lift  about  11  feet.  The  mean  barometric  pres- 
sure was  27.09  inches,  the  mean  temperature  91°  F.  The  results  of 
the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  13 — 12-foot  Aermotor. 
[Load  per  stroke,  330  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles  . 

36.7 

11.0 

39.6 

0.110 

16  miles 

57.0 

17.1 

61.6 

0.171 

20  miles  .   . 

70.0 

21.0 

75.6 

0.210 

25  miles     

82.0 

24.6 

88.6 

0.247 

30  miles 

91.7 

27.5 

99.0 

0.275 

The  important  difference  between  this  plant  and  No.  3  is  that  the 
latter  has  a  4-inch  supply  pipe  and  an  open  well,  while  the  former  has 
a  5-inch  supply  pipe  on  a  well  point.  The  useful  load  per  stroke  of 
mill  No.  13  is  20  per  cent  less  than  that  of  mill  No.  3,  and  the  num- 
ber of  strokes  per  minute  of  No.  13  is  slightly  greater  than  that  of 
No.  3.  It  appears  that  the  well  point  offers  some  resistance,  but  how 
much  can  not  be  said  from  this  data. 

Mitt  No.  14- — This  is  a  12-foot  Gem,  like  the  one  shown  in  PI.  IX,  on 
a  60-foot  steel  tower.  The  pump  is  of  the  Gause  make.  The  cylinder 
is  8  inches  in  diameter,  the  length  of  stroke  9  inches.  The  supply  is 
from  a  12-inch  pipe  in  an  open  well.  The  discharge  per  stroke  was 
9f  quarts  and  the  lift  15-J-  feet.  The  wind  velocity  was  not  measured. 

Mill  No.  15. — This  is  a  10-foot  Gem  similar  to  that  shown  in  PL  IX. 
The  tower  is  of  wood,  the  axis  of  the  wheel  being  34  feet  above  the 
ground.  The  mill  was  in  good  working  order,  but  the  exposure  was 
not  good,  on  account  of  trees.  The  wheel  has  24  sails,  each  36  by  11 
by  4f  inches,  set  at  an  angle  of  35°  with  the  plane  of  the  wheel. 
It  is  back-geared,  3  to  1.  The  pump  is  of  the  Stone  make.  The  dis- 
charge pipe  is  8  inches  in  diameter.  The  supply  pipe  is  on  a  3-inch 
well  point  8  feet  long,  the  lower  end  of  which  is  21^  feet  below  the  sur- 
face of  the  ground.  The  plunger  valve  is  of  the  single-flap  form. 
Depth  to  water  is  10  feet.  The  discharge  per  stroke  was  7  quarts,  the 
lift  about  15  feet.  The  mean  barometric  pressure  was  27.05  inches, 
the  mean  temperature  84°  F. 


lit 


MTIRPHY.I  PUMPING    MILLS    TESTED. 

The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  lf>— 10-foot  Gem. 
[Load  per  stroke,  219  foot-pounds.] 


43 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles 

23.4 

7.8 

13.6 

0.053 

16  miles  

35.7 

11.9 

21.0 

0.082 

20  miles 

44.1 

14.7 

25.7 

0.101 

25  miles        

43.8 

14.6 

25.5 

0.099 

This  mill  revolves  very  slowly,  indicating  a  heavy  load.  Its  useful 
horsepower,  however,  is  little  greater  than  that  of  mill  No.  5. 

Mill  No.  16. — This  is  a  10-foot  Halliday,  pumping  water  into  the 
same  pond  as  No.  15.  It  is  similar  to  the  mill  shown  in  fig.  20.  The 
tower  is  of  wood,  the  axis  of  the  wheel  being  28  feet  above  the  ground. 
The  wheel  has  78  sails,  each  36 \  by  4  by  2^  inches,  set  at  an  angle 
of  35.5°  to  the  plane  of  the  wheel.  It  is  not  back-geared.  The 
pump  is  of  the  Gause  make,  with  a  discharge  pipe  6  inches  in  diame- 
ter and  a  supply  pipe  4  inches  in  diameter.  There  is  a  6-inch  galvan- 
ized-iron  pipe,  forming  an  open  well,  extending  15  feet  into  the  water. 
The  depth  to  water  was  11  feet,  the  lift  16  feet,  and  the  discharge  per 
stroke  3  quarts.  The  mean  barometeric  pressure  was  27.02  inches, 
the  mean  temperature  94°  F.  The  results  of  tests  are  as  follows : 

Results  of  tests  of  mill  No.  16 — 10-foot  wooden  Halliday. 
[Load  per  stroke,  100  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles  

4.0 

4.0 

3.0 

0.012 

12  miles     . 

22.6 

22.6 

16.9 

0.067 

16  miles  

33.9 

33.9 

25.4 

0.103 

20  miles...  

42.7 

42.7 

32.0 

0.130 

25  miles          

52.5 

52.5 

39.3 

0.159 

This  10-foot  wooden  mill  is  seen  to  be  doing  more  useful  work  than 
the  10-foot  steel  Gem,  No.  15.  Usually,  however,  the  direct-stroke 
wooden  mills  do  less  work  than  the  back-geared  steel  mills  of  the  same 
size. 

Mill  No.  17. — This  is  a  12-foot  improved  Gem  on  a  30-foot  steel 
tower.  The  wheel  has  32  curved  sails,  each  42  by  11-J-  by  4f  inches, 
set  at  an  angle  of  37°  with  the  plane  of  the  wheel.  It  is  back-geared, 
2  to  1.  The  pump  is  of  the  Gause  type,  with  an  8-inch  discharge  pipe, 
a  4-inch  supply  pipe,  12  inches  stroke,  and  an  open  well  formed  of  a 
12- inch  wooden  casing.  The  depth  to  water  was  17^  feet,  and  the 


44 


THE    WINDMILL. 


[NO.  41. 


discharge  per  stroke  8f  quarts.  The  mean  barometric  pressure  was 
27.05  inches,  the  mean  temperature  93°  F.  The  results  of  the  tests 
are  as  follows : 

Results  of  tests  of  mill  No.  17 — 12- foot  improved  Gem. 
[Load  per  stroke,  385  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles 

12  0 

6  0 

12  7 

0  070 

16  miles 

25  6 

12  8 

27  2 

0  149 

20  miles 

34.6 

17.3 

36  8 

0  202 

This  mill,  although  nearly  new,  does  not  work  well.  It  is  out  of 
plumb.  Only  a  few  measurements  of  the  number  of  strokes  per  mile 
of  wind  were  made. 

Mill  No.  18. — This  is  an  8-foot  Ideal  on  a  36-foot  wooden  tower. 
The  exposure  was  good  and  the  parts  in  good  working  order.  The 
wheel  is  like  that  of  mill  No.  4.  The  pump  is  of  the  Stone  make,  with 
a  6-inch  discharge  pipe.  There  is  no  supply  pipe,  the  cylinder  being 
under  water,  with  3  inches  opening  to  it  from  below.  The  check  valve 
is  of  the  lift  variety,  the  plunger  valve  of  the  single-flap  variety.  The 
well  is  dug  to  a  depth  of  8  feet.  It  is  4£  feet  in  diameter.  In  the 
bottom  a  10-inch  galvanized-iron  pipe  extends  down  several  feet.  It 
was  11  feet  to  water.  The  lift  was  14  J  feet  and  the  discharge  per 
stroke  2.92  quarts.  The  mean  barometric  pressure  was  27.01  inches, 
the  mean  temperature  83°  F.  The  cost  of  the  plant,  including  pond, 
was  $125.  The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  18— 8-foot  Ideal. 

[Load  per  stroke,  89.2  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

20.0 

8.0 

5  8 

0  022 

12  miles 

50.5 

20.2 

14.6 

0.054 

16  miles 

65.2 

26.1 

18.9 

0.070 

20  miles  .      . 

70.0 

28.0 

20.3 

0.076 

25  miles  

68.7 

27.5 

19.9 

0.074 

After  the  spring  which  holds  the  wind  wheel  of  this  mill  in  the  wind 
was  tightened,  the  number  of  strokes  per  mile  of  wind  was  increased 
from  98  to  114  in  a  16-mile  wind,  from  84  to  102  in  a  20-mile  wind,  and 
from  66  to  79  in  a  25-mile  wind. 

Mill  No.  19.—  This  is  a  12-foot  Gem  (shown  in  PL  IX)  on  a  30-foot 
wooden  tower.  The  exposure  was  good  and  the  mill  in  good  work- 
ing order.  The  wheel  is  like  that  of  mill  No.  17.  The  pump  is  of 
the  Stone  make,  with  ;i  10-inch  discharge  pipe  and  a  4-inch  supply 


VIEW  OF   MILL  NO.   19— 12-FOOT  GEM. 


MURPHY.] 


PUMPING    MILLS    TESTED. 


45 


pipe.  The  length  of  the  stroke  is  10  inches.  The  supply  pipe  is  on  a 
4-inch  well  point  9  feet  long,  the  end  of  which  is  23  feet  below  the 
surface  of  the  ground.  The  check  valve  is  of  the  lift  type  and  the 
plunger  valve  of  the  single-flap  type.  The  lift  was  about  18  feet  and 
the  discharge  per  stroke  12  quarts.  The  mean  barometric  pressure 
was  27.13  inches,  the  mean  temperature  70°  F.  The  water  is  pumped 
into  a  reservoir  120  feet  by  60  feet.  The  results  of  the  tests  are  as 
follows : 

Results  of  tests  of  mill  No.  19— 12-foot  Gem. 

[Load  per  stroke,  450  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Stroke  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles 

12.4 

6.2 

18.6 

0.085 

16  miles 

23.8 

11.9 

35.7 

0.162 

20  miles 

29.4 

14.7 

44.1 

0.201 

25  miles 

32.0 

16.0 

48.0 

0.219 

This  curve  (fig.  18)  shows  that  a  9-mile  wind  is  necessary  to  start 
this  mill,  and  that  the  greatest  number  of  strokes  per  mile  of  wind 


10 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

15  20 


40 


30 


FIG.  18.— Diagram  showing  results  with  mill  No.  19— 12-foot  Gem. 

is  45 — about  25  per  cent  less  than  most  12-foot  steel  back-geared  mills, 
being  at  the  rate  of  6  strokes  at  12  miles  and  16  strokes  at  25  miles  an 
hour.  The  load  of  this  mill  is  somewhat  greater  than  that  of  No.  3, 
and  its  power  should  be  equal  or  greater,  but  it  is  seen  to  be  much  less. 


U.    S.   GEOLOGICAL  SURVEY 


WATER-SUPPLY  PAPER  NO.    41       PL.   XI 


VIEW   OF   MILL   NO.   21— 12-FOOT   HALLIDAY. 


MURPHY.] 


PUMPING    MILLS    TESTED. 


47 


Mitt  No.  %!.—  This  is  a  12-foot  Halliday  (shown  in  PI.  XI)  on  a  31- 
foot  wooden  tower.  It  was  made  by  the  United  States  Wind  Engine 
and  Pump  Company,  of  Batavia,  Illinois.  The  working  parts  are 


FIG.  20.-Working  parts  of  Halliday  mill:  A,  bed  plate;  A',  fan  arm;  £,  turntable;  B',  regu- 
lating rod;  C,  front  plate;  C",  assisting  weight;  A  sliding  head ;  E,  tie  rod;  F,  forked  lever;  F', 
fans  or  sails;  G,  truss  frame;  H,  truss  rod;  L,  pitman;  I/,  fan  lever;  If,  crank  plate;  31'  If', 
masts;  P,  weight  lever;  R,  shut-off  rod ;  R' ,  shut-off  rod  lever;  S,  main  shaft;  -S",  sleeve;  F,  vane; 
F',  vane  arm;  TT,  weight;  W,  counterweight;  JT,  swivel  box;  F,  spider;  Z,  sliding  box. 

shown  in  fig.  20.  The  wheel  has  64  sails,  each  42|  by  5  by  2f  inches, 
set  at  an  angle  of  35°  with  the  plane  of  the  wheel.  It  is  not  back- 
geared,  and  regulates  itself  on  the  centrifugal  principle — the  sails 


48 


THE    WINDMILL. 


[NO.  41. 


taking  the  direction  of  the  wind.  The  pump  is  of  the  Stone  make, 
with  7|-inch  discharge  pipe,  4-inch  supply  pipe,  and  7  inches  stroke. 
The  check  valve  is  of  the  lift  variety,  the  plunger  valve  of  the 
double-flap  variety.  The  well,  which  is  open,  is  formed  by  a  wooden 
curb,  12  inches  in  diameter,  sunk  in  the  bottom  of  a  dug  well  9  feet 
deep.  The  depth  to  water  was  11£  feet  and  the  lift  11  feet.  The  dis- 
charge per  stroke  was  4-J  quarts  when  pumping  quite  rapidly  (30 
strokes  per  minute).  The  valves  were  not  in  very  good  repair  and 
the  pump  lost  its  priming  after  a  time.  The  results  of  the  tests  are 
as  follows: 

Results  of  tests  of  mill  No.  21 — 12-foot  wooden  Halliday. 
[Load  per  stroke,  141.5  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles..  _.  .  . 

14.0 

14.0 

15  9 

0  060 

16  miles 

28  5 

28  5 

32  1 

0  121 

20  miles  . 

37.3 

37  3 

42  0 

0  159 

25  miles  

44.6 

44.6 

50  2 

0  184 

This  curve  (shown  in  fig.  21),  which  is  for  a  lightly  loaded  (141.5 
foot-pounds)  direct-stroke  12-foot  mill,  will  be  seen  to  start  at  a  wind 


10 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 
15  30 


130 


100 


80 


FIG.  21.— Diagram  showing  results  with  mill  No.  31— 12-foot  Halliday. 

velocity  of  9  to  10  miles  and  to  reach  a  maximum  at  19  miles,  with  a 
speed  of  112  strokes  per  mile.     At  30  miles  the  number  of  strokes  is 


MURPHY.] 


PUMPING    MILLS    TESTED. 


49 


about  98  per  mile.  The  number  of  strokes  per  minute  varies  from  14 
at  12  miles  to  45  at  25  miles.  The  power  of  this  mill  is  only  about 
half  that  of  the  12-foot  Aermotor,  No.  3. 

Mill  No.  25. — This  is  an  8-foot  steel  mill  on  a  32-foot  steel  tower, 
made  by  Fairbanks,  Morse  &  Company.  The  wheel  has  18  curved  sails, 
each  29  by  llf  by  5£  inches,  set  at  an  angle  of  29°  with  the  plane 
of  the  wheel.  It  is  back-geared,  2^  to  1.  The  pump  is  of  the  com- 
mon hand  variety,  with  a  2^-inch  cylinder,  1^-inch  supply  and  dis- 
charge pipes,  and  4  inches  stroke.  The  well  is  open,  6J  feet  to  water. 
The  discharge  per  stroke  was  0. 31  quart  and  the  lift  8-J  feet.  The 
water  raised  is  used  for  watering  stock.  The  results  of  the  tests  are 
as  follows: 

Results  of  tests  of  mill  No.  25— 8-foot  Fairbanks-Morse  steel  mill. 
[Load  per  stroke,  5.5  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

30.7 

12  3 

1  0 

0  002 

12  miles  

73.0 

29  2 

2  3 

0  005 

16  miles  

93.2 

37.3 

2  9 

0  007 

20  miles  . 

95.0 

38  0 

3  0 

0  008 

25  miles.  

83.2 

33.3 

2  6 

0  005 

VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 
10  15  20 


25 


o 
co   20 


This  is  a  very  lightly  loaded  mill — only  5.5  foot-pounds  per  stroke  of 
pump.  The  number  of  strokes 
per  minute  in  light  winds  is 
large;  the  number  of  strokes  per 
minute  in  a  25-mile  wind  is  only 
33.3,  compared  with  38  in  a 
20-mile  wind.  A  comparison  of 
this  mill  with  No.  5  will  show 
the  difference  between  a  small 
pumping  outfit  for  stock  pur- 
poses and  one  for  irrigation. 

Mill  No.  30.—  This  is  a  16-foot 
Irrigator  manufactured  by  M. 
Schow,  of  Kinsley,  Kansas.  It  is 
a  power  mill,  but  not  geared  for- 
ward, and  works  a  pump  called  a 
' '  water  elevator. "  The  tower  is 
of  wood,  22  feet  to  axis  of  wheel. 
The  wind  wheel  has  10  plane 
wooden  sails,  each  70£  by  16  by 
13£  inches,  set  at  an  angle  of 
39°  to  the  direction  of  the  wind. 
The  vertical  shafting  is  geared  back  30  to  13,  and  the  horizontal  shaft 
is  geared  forward  13  to  30.  The  water  is  lifted  from  a  well  8  feet 
IRR  41—01 4 


o 

£    10 

9 


FIG.  22.  —Diagram  showing  revolutions  of  wind 
wheel  of  mill  No.  30— 16-foot  Irrigator.  AB  is 
for  a  load  of  32  foot-pounds  per  revolution  of 
wind  wheel;  CD  is  for  a  load  of  251  foot-pounds; 
ED  is  for  a  useful  pump  load  of  337  foot-pounds. 


50 


THE    WINDMILL. 


[NO.  41. 


by  10  feet  (7  feet  depth  to  water),  cased  with  wood.  The  buckets 
of  the  elevator  are  made  of  galvanized  iron  and  are  14  by  7-J-  by  5-j- 
inches,  set  18  inches  center  to  center,  and  hold  3  gallons  each.  Each 
bucket  has  a  valve  in  its  bottom.  The  lift  is  about  11  feet,  and  there 
are  20  buckets  on  the  elevator  chains.  There  is  a  box  in  fche  bottom 
of  the  well  into  which  the  buckets  dip  to  get  their  supply  of  water. 
This  box  has  a  screen  in  its  bottom  to  keep  out  the  sand.  The  mill 
does  not  govern  well,  on  account  of  side  draft.  The  mean  barometric 
pressure  was  27.7  inches,  the  mean  temperature  72°  F.  The  results 
of  the  tests  are  as  follows : 

Results  of  tests  of  mill  No.  30— 16-foot  Irrigator. 


Load  on 
brake. 

Load 
per  rev- 
olution 
of  wind 
wheel. 

Number  of  revolutions  of  wind  wheel 
per  minute  at  given  wind  velocities 
(per  hour). 

Useful  horsepower   at    given  wind 
velocities  (per  hour). 

8 
miles. 

12 

miles. 

15 
miles. 

30 
miles. 

25 
miles. 

8 
miles. 

13 
miles. 

15 
miles. 

20 
miles. 

25 
miles. 

Pounds. 
2 
16 
Pump. 

Ft.-lbs. 
32 
251 
837 

12 

26 
19 
14 

33 

39 
36 

41 
39 

38 

44 

4/W 

43 

0.013 

0.025 
0.140 
0.140 

0.032 
0.220 
0.250 

0.040 
0.300 
0.400 

0.043 
0.320 
0.440 

.2 


Fig.  22  shows  the  number  of  revolutions  per  minute  of  the  wind 

wheel  for  three  loads.     Fig.  23  shows  the  horsepower  for  these  loads. 

VELOCITY  OF  WIND  IN  MILES  PER  HOUR.         Comparing    the     useful    pump 

10  15  20  25    horsepower   of    this    mill   with 

that  of  the  16-foot  mill  No.  9, 
it  will  be  seen  that  this  mill  is 
not  so  powerful  as  No.  9.  The 
power  of  the  Aermotor  for  low 
velocities  is  much  greater  than 
that  of  the  Irrigator. 

Mill  No.  31.—  This  is  a  14-foot 
Elgin  wooden  power  mill,  manu- 
factured at  Elgin,  Illinois.  It 
works  a  rotary  (Wonder)  pump. 
The  wind  wheel  is  on  a  48-foot 
wooden  tower.  It  has  88  plane 
wooden  sails,  each  52  by  G  by 
34  inches,  set  at  an  angle  of  37° 
to  the  plane  of  the  wheel.  It 
is  a  sectional  vaneless  wheel; 
in  place  of  the  vane  there  is  a 
heavy  counterpoise.  The  wheel 
is  geared  forward  about  7.19  to 
1.  The  rotary  pump  is  a  3  inch.  It  is  on  a  well  point  G  inches  in 
diameter  and  8  feet  long;  the  point  penetrates  the  water  to  a  deptli  of 
8  feet.  The  lift  was  about  18  feet.  The  suction  and  discharge  pipes 


FIG.  23.— Diagram  showing  horsepower  of  mill 
No.  30.  Curve  AB  shows  the  horsepower  for  a 
33  foot-pound  load;  CD,  the  power  for  a 251  foot- 
pound load ;  EF,  the  power  for  a  3137  foot-pound 
load ;  dotted  curve  shows  maximum  horsepower 
for  best  load. 


MUKPHY.] 


PUMPING    MILLS    TESTED. 


51 


are  each  3  inches  in  diameter.  The  discharge  was  2  quarts  per  revo- 
lution of  pump.  The  pump  is  manufactured  by  the  National  Pump 
Company,  of  Kansas  City,  Missouri.  In  a  15-mile  to  a  20-mile  wind 
the  windmill  worked  the  pump  before  priming,  but  would  not  start  it 
in  that  wind  after  priming.  After  several  attempts  of  the  mill  to 
start  the  pump  the  pulley  turned  on  the  shaft  so  that  it  could  not  be 
used.  It  was  very  evident  that  the  pump  was  too  great  a  load  for  the 
mill.  The  owner  stated  that  the  mill  would  only  run  during  a  strong 
wind. 

Mill  No.  32. — This  mill  is  like  the  12-foot  Aermotor,  the  working 
parts  of  which  are  shown  in  fig.  7.  It  is  on  a  40-foot  steel  tower. 
The  wheel  has  18  curved  sails,  each  44  by  18f  by  7f  inches,  set  at  an 
angle  of  31°  to  the  plane  of  the  wheel.  The  pump  is  of  the  Wood- 
manse  t}7pe,  a  sectional  view  of  which  is  shown  in  fig.  5,  and  has  an 
8-inch  cylinder  and  12  inches  stroke.  It  is  in  an  open  well.  The  depth 
to  water  was  14  feet,  the  lift  20  feet,  and  the  discharge  per  stroke  7 
quarts.  It  is  back-geared,  3£  to  1.  The  water  is  pumped  into  a  pond 
and  used  for  irrigation.  The  mean  barometric  pressure  was  27.9 
inches,  the  mean  temperature  82°  F.  The  results  of  the  tests  are  as 
follows : 

Results  of  tests  of  mill  No.  32 — 12-foot  Aermotor. 
[Load  per  stroke,  313  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

Smiles  

17.7 

5.3 

9.3 

0.047 

12  miles 

49.3 

14  8 

25.9 

0  131 

15  miles 

60.0 

18.5 

32.4 

0.164 

20  miles 

73.0 

22.0 

38.5 

0.195 

Mill  No.  33 — This  is  a  10-foot  Woodmanse  pumping  mill  on  a  40-foot 
steel  tower.  The  working  parts  are  like  those  shown  in  fig.  4.  The 
wheel  has  24  curved  sails,  each  30^  by  12|  by  5^  inches,  set  at  an 
angle  of  29°  to  the  plane  of  the  wheel.  It  is  back-geared,  2-j-  to  1. 
The  pump  is  of  the  Woodmanse  make  (like  that  shown  in  fig.  5),  with 
a  6-inch  cylinder  and  10  inches  stroke.  The  depth  to  water  was  14 
feet.  The  pump  is  on  a  well  point  3£  inches  in  diameter,  4  feet  long, 
and  67  feet  below  the  surface  of  the  ground.  The  suction  pipe  is  3£ 
inches  in  diameter,  the  discharge  pipe  6  inches  in  diameter.  The  lift 
was  about  22  feet,  the  discharge  per  stroke  3f  quarts.  The  water 
is  pumped  into  a  pond  and  used  for  irrigation.  The  mean  barome- 
tric pressure  was  27.9  inches,  the  mean  temperature  88°  F. 


52  THE    WINDMILL. 

The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No*  33 — 10-foot  Woodmanse. 
[Load  per  stroke,  173  foot-pounds.] 


[NO.  41. 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

8.7 

3.5 

3.3 

0.020 

12  miles          

36.0 

14.4 

13.5 

0.075 

15  miles 

51.2 

20.5 

19.2 

0.110 

Mill  No.  35. — This  is  an  8-foot  steel  Dempster  pumping  mill,  manu- 
factured by  the  Dempster  Manufacturing  Company,  of  Beatrice, 
Nebraska,  and  is  shown  in  PI.  XII.  The  tower  is  of  steel,  80  feet  to  axis 
of  wheel.  The  wind  wheel  has  18  curved  sails,  each  30£  by  14-j-  by  7 
inches,  set  at  an  angle  of  27°  to  the  plane  of  the  wheel.  It  is  back- 
geared,  3  to  1.  The  well  is  an  open  dug  well.  The  distance  from  the 
surface  of  the  ground  to  the  water  was  39  feet.  The  water  is  pumped 
into  a  tank  22  feet  above  ground,  and  is  used  for  irrigation.  The 
pump  has  an  8-inch  stroke,  a  3^-inch  cylinder,  and  2-inch  suction  and 
discharge  pipes.  The  lift  was  58  feet,  the  discharge  per  stroke  1.1 
quarts.  The  mean  temperature  was  51°  F. ,  the  mean  barometric  pres- 
sure 28.9  inches.  The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  35 — 8-foot  steel  Dempster. 
[Load  per  stroke,  133.5  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

12  miles 

57.6 

19.2 

5.3 

0.077 

16  miles             

86.4 

28.8 

7.9 

0.116 

20  miles 

99.9 

33.3 

9.2 

0.134 

In  a  15-mile  wind  the  pump  made  26  to  27  strokes  per  minute,  and 
when  the  pump  rod  was  uncoupled  from  the  pump  it  made  34  strokes 
per  minute  in  the  same  wind.  Fig.  24  shows  the  number  of  strokes 
per  minute  for  different  wind  velocities.  This  mill  is  heavily 
loaded — 133  foot-pounds  per  stroke  of  pump.  It  starts  at  a  wind 
velocity  of  about  9  miles  an  hour,  and  as  the  wind  increases  the 
number  of  strokes  increases  rapidly  at  first,  then  more  slowly.  At 
25  miles  an  hour  the  number  of  strokes  is  37  per  minute.  This  mill 
is  back-geared,  3  to  1,  so  that  in  a  25-mile  wind  the  wind  wheel  makes 
111  revolutions  per  minute  and  has  a  circumference  velocity  of  46.5 
feet  per  second. 

Mill  No.  36. — This  is  a  22|-foot  Eclipse  wooden  pumping  mill,  lift- 


U.    S.    GEOLOGICAL  SURVE 


VIEW   OF   MILL   NO.  35— 8-FOOT   DEMPSTER. 


MURPHY.] 


PUMPING    MILLS    TESTED. 


53 


40 


30 


ing  water  into  a  tank  for  railroad  purposes.  The  tower  is  of  wood,  52 
feet  to  the  axis  of  the  wheel.  The  wind  wheel  has  136  plane  sails, 
each  105  by  6  by  2  inches,  set  at  an  angle  of  39°  to  the  plane  of  the 

Wheel.      It    works    by  direct  VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

stroke.     The  well,  which  is  in  15  20  25 

open,  is  20  feet  in  diameter; 
the  depth  to  water  was  19 
feet  from  the  surface  of  the 
ground.  The  pump  is 
double-acting,  and  has  a 
44-inch  cylinder,  7  inches 
stroke,  and  2-inch  suction 
and  discharge  pipes.  The 
lift  was  39  feet.  The  tank 
is  90  feet  from  the  well. 
The  discharge  could  not  be 
measured,  but  as  the  pack- 
ing of  the  pump  was  new  it 
was  approximately  equal  to 
twice  the  volume  of  the 


10 


FIG.  24. — Comparative  diagram  showing  results  with 
mills  No.  35  (8-foot  Dempster)  and  No.  36  (22Hoot 
Eclipse). 


cylinder,  or  0.76  gallon  per  double  stroke.  The  mean  temperature 
was  58°  F.,  the  mean  barometric  pressure  29.43  inches.  The  results 
of  the  tests  are  as  follows : 

Results  o/  tests  o/  mill  No.  36 — 22%-foot  wooden  Eclipse. 
[Load  per  stroke,  248  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles  

4.8 

4.8 

3.8 

0.036 

12  miles 

12.0 

12.0 

9.4 

0.090 

16  miles. 

16.5 

16.5 

12.8 

0.124 

20  miles..  . 

20.0 

20.0 

15.6 

0.150 

25  miles 

24.2 

24.2 

18.8 

0.182 

Fig.  24  shows  the  strokes  per  minute  at  different  wind  velocities. 
The  diagram  is  seen  to  be  quite  different  from  that  of  mill  No.  35. 
The  mill  starts  at  a  wind  velocity  of  6  or  7  miles  an  hour,  and 
increases  gradually  to  24  strokes  in  a  25-mile  wind.  The  circumfer- 
ence velocity  of  the  latter  is  46.5  feet  per  second,  that  of  the  former 
29  feet.  The  wind  wheel  of  this  mill  is  making  24  revolutions  per 
minute;  that  of  No.  35  is  making  111  revolutions  per  minute  in  a 
25-mile  wind. 

Mitt  No.  37.—  This  is  a  12-foot  steel  Woodrnanse  Mogul  like  that 
shown  in  fig.  4.  It  pumps  water  into  a  pressure  tank  9-J-  feet  by  2£  feet 
in  a  cellar  and  about  170  feet  from  the  well.  The  pump  and  pressure 


54 


THE    WINDMILL. 


[NO  41. 


tauk  are  shown  in  fig.  25.  The  tower  is  of  steel,  and  is  40  feet  to  the 
axis  of  the  wheel.  The  wind  wheel  has  30  curved  sails,  each  37  by  13 
by  5.5  inches,  set  at  an  angle  of  29°  to  the  plane  of  the  wheel.  The 
well  is  50  feet  deep  and  8  inches  in  diameter;  the  depth  to  water  was 
42  feet.  The  pump  has  a  3-inch  cylinder  and  9  inches  stroke.  The 
discharge  pipe  is  1  inch  in  diameter,  the  suction  pipe  1£  inches  in 


FIG.  25.—  Pump,  pressure  tank,  and   hydraulic  regulator  of  mill  No.  37 -12  foot  Woodnmnse 

Mogul. 

diameter.  The  discharge  per  stroke  was  1.05  quarts.  The  load  on 
the  pump  was  equal  to  43  feet  head  of  water  (the  friction  in  about 
200  feet  of  1-inch  pipe)  and  a  compressed-air  pressure  the  amount  of 
which  was  recorded  on  a  gage.  The  mean  temperature  was  00°  F.,  the 
mean  barometric  pressure  29.1  inches.  The  results  of  the  tests  are  as 
follows : 


MURPHY.]  PUMPING   MILLS   TESTED. 

Results  of  tests  of  mill  No.  37 — 12-foot  steel  Woodmanse  Mogul. 


55 


6 

1 

Number  of  strokes  of  pump  per  min- 
ute  at  given  wind   velocities  (per 
hour). 

Useful  horsepower  at  given  wind 
velocities  (per  hour). 

8  miles. 

12  miles. 

16  miles. 

20  miles. 

1 

i 

8 

30  miles. 

8  miles. 

12  miles. 

16  miles. 

1 

i 

8 

1 

i 

& 

1 
1 

8 

Ft.-lbs. 
94 
254 
350 
473 

7.7 

18.4 
12.2 

24.5 
19.0 

29.3 
23.3 
18.0 
10.7 

34.2 
26.7 
21.0 

38.0 
29.0 
21.5 

0.022 

0.053 
0.094 

0.071 
0.146 

0.083 
0.180 
0.191 
0.153 

0.097 
0.205 
0.223 

0.108 
0.223 
0.228 

Fig.  26  shows  the  number  of  strokes  per  minute  for  different  wind 
velocities  for  four  useful  pump  loads,  viz,  43  feet,  43  feet  plus  32 
pounds,  43  feet  plus  50  pounds,  and  43  feet  plus  75  pounds,  or, 
reducing  the  pounds  pressure  to  head  in  feet,  the  four  useful  loads 
are:  43  feet  for  the 


curve  aa',  116  feet  for 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

10  15  20  25 


the  curve  bb',  160  feet 
for  the  curve  cc',  and 
216  feet  for  the  curve 
dd'.  The  effect  of  in- 
creased load  on  the 
number  of  strokes  is 
well  shown  here.  The 
effect  of  the  hydraulic 
regulator  may  be  seen 
in  the  curve  cc',  but  it 
is  shown  to  a  greater 
extent  in  the  curve 
dd'. 

Mill  No.  38.—  This 
is  a  10-foot  Woodmanse  wooden  mill  on  a  30-foot  wooden  tower,  and  is 
used  to  pump  water  for  stock.  The  wind  wheel  has  96  plane  sails, 
each  34  by  3|  by  1£  inches,  set  at  an  angle  of  38°  to  the  plane  of  the 
wheel.  The  well  is  driven  and  is  107  feet  deep;  the  depth  to  water 
was  about  44  feet.  The  pump  works  direct  and  has  a  2^-inch  cylinder 
and  4  inches  stroke.  The  lift  was  about  50  feet,  and  the  discharge 
per  stroke  of  pump  -fa  gallon. 


PIG.  26.— Diagram  showing  results  with  mill  No.  37— 12- foot 
Woodmanse  Mogul.  The  curve  aa'  is  for  a  useful  pump  load 
of  43  feet  head;  bb'  is  for  a  useful  pump  load  of  116  feet  head; 
cc'  is  for  a  useful  pump  load  of  160  feet  head;  dd'  is  for  a  use- 
ful pump  load  of  216  feet  head.  The  effect  of  the  hydraulic 
regulator  is  shown  in  the  curves  cc'  and  dd'. 


56  THE    WINDMILL. 

The  results  of  the  tests  are  as  follows : 

Results  of  tests  of  mill  No.  38— 10-foot  wooden  Woodmanse. 
[Load  per  stroke,  21  foot-pounds.] 


[NO.  41. 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute, 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

18 

18 

0  9 

0  012 

12  miles  .  .          . 

29 

29 

1.5 

0.019 

16  miles  

36 

36 

1.8 

0.023 

20  miles 

41 

41 

2  1 

0  026 

25  miles 

46 

46 

2.3 

0.029 

Fig.  27  shows  the  number  of  strokes  per  minute  for  different  wind 
velocities.     This  is  a  lightly  loaded  mill,  working  direct  stroke.     It 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

10  15  20  25 


50 


10 


FIG.  27.— Comparative  diagram  showing  results  with  mills  No.  38  (10-foot  wooden  Woodmanse) 
and  No.  48  (30-foot  wooden  Halliday). 

starts  in  a  5-mile  wind ;  the  number  of  strokes  increases  very  rapidly 
at  first,  and  more  slowly  for  high  velocities.  In  a  30-mile  wind  the 
number  of  strokes  per  minute  is  50.  The  circumference  velocity 
of  this  wheel  in  a  25-mile  wind  is  24  feet  per  second. 

Mill  No.  39. — This  is  a  10-foot  Woodmanse  direct-stroke  iron  pump- 
ing mill,  used  to  pump  water  for  stock.  The  tower  is  of  iron,  35  feet 
to  the  axis  of  the  wheel.  The  wind  wheel  has  18  curved  sails,  each  30 
by  12£  by  7f  inches,  set  at  an  angle  of  40°  to  the  plane  of  the  wheel. 
The  pump  is  on  a  well  point  24  feet  below  the  surface  of  the  ground. 
It  has  a  stroke  of  6  inches,  a  3^-inch  cylinder,  and  1^-inch  suction 
and  discharge  pipes.  The  lift  was  about  27  feet,  the  discharge  per 
stroke  1  quart.  The  results  of  the  tests  are  as  follows : 


MURPHY.] 


PUMPING    MILLS    TESTED. 


57 


Results  of  tests  of  mill  No.  39— 10-foot  iron  Woodmanse. 
[Load  per  stroke, 36  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

15 

15 

3.7 

0.017 

12  miles        

30 

30 

7.5 

0.034 

16  miles 

40 

40 

10.0 

0.044 

20  miles      .          ... 

47 

47 

11.7 

0.052 

Mill  No.  40. — This  is  an  8-foot  steel  pumping  mill  manufactured  by 
Fairbanks,  Morse  &  Company.  It  is  used  to  pump  water  for  stock.  It 
is  on  a  30-foot  steel  tower.  The  wind  wheel  has  18  curved  sails,  each 
29  by  10^  by  5  inches,  set  at  an  angle  of  29°  to  the  plane  of  the  wheel. 
It  is  back-geared,  2^-  to  1.  The  pump  is  on  a  well  point  20  feet  below 
the  surface  of  the  ground.  It  has  a  stroke  of  6  inches,  a  3^-inch 
cylinder,  and  1^-inch  suction  and  discharge  pipes.  The  lift  was  about 
22  feet,  and  the  discharge  per  stroke  -^  gallon.  The  results  of  the  tests 
are  as  follows : 

Results  of  tests  of  mill  No.  40 — 8-foot  Fairbanks-Morse  steel  mill. 
[Load  per  stroke,  13  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

32.5 

13.0 

0.8 

0.005 

12  miles.      .     ...  

55.0 

22.0 

1.5 

0.009 

16  miles 

72.0 

29.0 

1.9 

0  012 

20  miles 

85.0 

34.0 

2.3 

0.014 

Mill  No.  Jt-1. — This  is  a  12-foot  Woodmanse  direct-stroke  iron  pump- 
ing mill,  used  for  pumping  water  for  stock.  The  tower  is  of  iron,  30 
feet  to  the  axis  of  the  wheel.  The  pump  has  a  3-inch  cylinder  and  6 
inches  stroke.  The  wind  wheel  has  24  curved  sails,  each  36  by  14-J  by 
7f  inches,  set  at  an  angle  of  39°  to  the  plane  of  the  wheel.  The  lift 
was  28  feet,  and  the  discharge  per  stroke  ^  gallon.  The  results  of  the 
tests  are  as  follows : 

Results  of  tests  of  mill  No.  41 — 12-foot  iron  Woodmanse. 
[Load  per  stroke,  29  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

14 

14 

1   7 

0  012 

12  miles 

25 

25 

3  1 

0  022 

16  miles.   ..   

33 

33 

4.1 

0  029 

20  miles  . 

40 

40 

5  0 

0  036 

58 


THE    WINDMILL. 


[NO.  41. 


Mill  No.  4%- — This  is  a  6-foot  Ideal  pumping  mill  on  a  22-foot  steel 
tower,  and  is  used  for  pumping  water  for  stock.  It  is  shown  in  PI. 
XIII.  The  wheel  has  12  curved  sails,  each  26  by  14£  by  5  inches,  set 
at  an  angle  of  39°  to  the  plane  of  the  wheel.  It  is  back-geared,  4  to  1. 
The  well  is  a  dug  well;  depth  to  water,  15  feet.  The  pump  has  a  3-inch 
cylinder  and  6  inches  stroke.  The  lift  was  16  feet,  the  discharge  per 
stroke  1  quart.  The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  42— 6-foot  Ideal. 
[Load  per  stroke,  35  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

16 

4 

1.0 

0  004 

12  miles 

52 

13 

3.2 

0  014 

16  miles  .._  

76 

19 

4.7 

0.020 

20  miles  -  

92 

23 

5.7 

0.024 

FKJ.  as.—  View  of  mill  No.  43— 10-foot  Perkins. 


This  is  the  smallest  mill  yet  tested.  It  is  rather  heavily  loaded  for 
its  size;  in  fact,  it  is  more  heavily  loaded  than  the  12-foot  mill  No. 
41.  It  is  doing  very  good  work  for  a  mill  of  its  size. 


MURPHY.] 


PUMPING    MILLS   TESTED. 


59 


Mill  No.  43.—  This  is  a  10-foot  Perkins  direct-stroke  pumping  mill 
on  a  32-foot  steel  tower,  and  is  used  to  pump  water  for  stock.  The 
working  parts  are  shown  in  fig.  28.  The  wind  wheel  has  30  curved 
sails,  each  30  by  10J-  by  5  inches,  set  at  an  angle  of  29°  to  the  plane 
of  the  wheel.  The  pump  is  on  a  well  point  34  feet  below  the  surface 
of  the  ground.  It  has  a  3-inch  cylinder  and  4  inches  stroke.  The 
lift  was  about  36  feet,  the  discharge  per  stroke  |  quart.  The  exposure 
was  not  good.  The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  43— 10-foot  Perkins. 

[Load  per  stroke,  37  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

20 

20 

2.5 

0.022 

12  miles 

32 

32 

4.0 

0.035 

16  miles    

41 

41 

5.1 

0.045 

20  miles  

45 

45 

5.6 

0.050 

Mill  No.  4$- — This  is  a  10-foot  Eclipse  direct-stroke  pumping  mill 
used  to  pump  water  for  stock.  The  tower  is  of  wood,  40  feet  to  the 
axis  of  the  wheel.  The  wind  wheel  has  84  plane  sails,  each  36£  by  4  by 
1£  inches,  set  at  an  angle  of  35°  to  the  plane  of  the  wheel.  The  well 
is  a  (Jug  well;  depth  to  water,  12  feet.  The  pump  has  a  stroke  of  6 
inches,  a  3-inch  cylinder,  and  1/J-inch  suction  and  discharge  pipes. 
The  lift  was  14  feet,  and  the  discharge  per  stroke  0.62  quart.  The 
results  of  the  tests  are  as  follows : 

Results  of  tests  of  mill  No.  45 — 10-foot  wooden  Eclipse. 
[Load  per  stroke,  18  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles  _.  

18 

18 

2.8 

0.010 

12  miles  . 

28 

28 

4.3 

0.014 

16  miles   

32 

32 

5.0 

0.016 

20  miles 

35 

35 

5.4 

0.018 

25  miles 

38 

38 

5.9 

0.019 

Mill  No.  46- — This  is  a  10-foot  Cornell  direct-stroke  wooden  mill 
manufactured  at  Louisville,  Kentucky,  and  is  used  to  pump  water 
for  stock.  The  tower  is  of  wood,  30  feet  to  the  axis  of  the  wheel.  The 
wind  wheel  has  90  plane  sails,  each  36  by  4£  by  1-J  inches,  set  at  an 
angle  of  47°  to  the  plane  of  the  wheel.  The  well  is  a  dug  well;  the 
water  is  only  about  3  feet  below  the  surface  of  the  ground.  The 
pump  has  a  3^-inch  cylinder  and  4  inches  stroke.  The  discharge 


60 


THE    WINDMILL. 


(NO.  41 . 


per  stroke  was  1  pint  when  pumping  rapidly.     The  lift  was  5f  feet. 
The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  46— 10-foot  wooden  Cornell. 
[Load  per  stroke,  6  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles   

16 

16 

2.0 

0.003 

12  miles 

25 

25 

3  1 

0.004 

16  miles 

36 

36 

4.5 

0.006 

20  miles              .  . 

42 

42 

5.2 

0.007 

25  miles  -  

48 

48 

6.0 

0.007 

30  miles  

52 

52 

6.5 

0.008 

Mill  No.  47- — This  is  a  10-foot  Dempster  steel  mill,  like  that  shown 
in  PL  XII,  on  a  40-foot  steel  tower.  The  wind  wheel  has  24  curved 
sails,  each  30-J-  by  13£  by  6£  inches,  set  at  an  angle  of  29°  to  the  plane 
of  the  wheel.  The  pump  is  back-geared,  2J-  to  1,  and  has  a  3-inch 
cylinder  and  7  inches  stroke.  The  well  is  open,  20f  feet  to  water,  and 
situated  under  the  porch  of  a  house.  The  mill  is  located  76  feet  from 
the  well.  The  cylinder  is  directly  under  the  mill,  in  a  chamber  4  feet 
by  4  feet,  and  6  feet  deep.  The  lower  end  of  the  cylinder  was  about 
12  feet  vertically  above  the  surface  of  the  water  in  the  well.  The 
discharge  per  stroke  was  1  quart  when  pumping  rapidly.  The  lift 
was  about  18  feet.  The  wind  wheel  of  this  mill  is  not  well  balanced, 
and  the  spring  which  holds  it  in  the  wind  is  not  stiff  enough.  The 
results  of  the  tests  are  as  follows : 

Results  of  tests  of  mill  No.  47— 10-foot  steel  Dempster. 
[Load  per  stroke,  37  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

37 

13 

3.2 

0.014 

12  miles 

66 

23 

5.7 

0.026 

16  miles  .     . 

89 

31 

7.8 

0.035 

20  miles 

95 

33 

8.3 

0.037 

25  miles 

0 

0 

0 

0.000 

A  diagram  which  was  platted  for  this  mill  shows  that  the  curve 
drops  at  about  19  miles  an  hour,  and  reaches  the  axis  line  at  24  miles. 
Above  24  miles  an  hour  the  wheel  is  entirely  out  of  the  wind  and  does 
no  work.  On  this  diagram  was  also  platted  the  number  of  strokes 
per  minute  of  the  8-foot  Dempster  (No.  35),  to  show  the  effect  of  the 
different  loads  upon  the  number  of  strokes  per  minute.  The  8-foot 
mill  was  found  to  be  carrying  more  than  three  times  the  load  that  the 
10-foot  mill  was  carrying. 


U.    S.    GEOLOGICAL  SURVEY 


'ATER-SUPPLY  PAPER  NO.   41        PL.    XIV 


VIEW   OF    MILL    NO.   48-30-FOOT    HALLIDAY. 


MUKPHY.] 


PUMPING    MILLS    TESTED. 


61 


Mill  No.  48. — This  is  a  30-foot  Halliday  wooden  pumping  mill  on  a 
70-foot  wooden  tower.  It  is  owned  by  the  city  of  Valley  Falls,  Kansas, 
and  is  used  to  pump  water  for  the  city  supply.  The  mill  and  tower 
are  shown  in  PL  XIV.  The  sail  area;  is  arranged  in  two  concentric 
rings.  In  the  outer  ring  there  are  192  sails,  in  the  inner  ring  144 
sails,  each  43  by  4-J  by  3^  inches,  set  at  an  angle  of  25°  to  the  plane  of 
the  wheel.  There  are  two  wells;  one  (11  feet  in  diameter)  directly 
under  the  mill,  and  another  (10  feet  in  diameter)  near  the  bank  of 
the  river  375  feet  from  the  mill.  A  3-inch  suction  pipe  connects  the 
wells,  and  a  3-inch  supply  pipe  leads  from  the  lower  well  to  the  river. 
The  pump  is  double-acting,  and  has  a  4-inch  cylinder  and  11  inches 
stroke.  The  water  is  pumped  directly  into  the  distribution  pipes, 
also  into  an  elevated  tank.  The  tank  is  of  wood,  20  feet  by  30  feet, 
and  is  5,570  feet  distant  from  the  mill.  Of  the  connecting  pipe,  50 
feet  is  3  inches  in  diameter,  1,200  feet  is  4  inches  in  diameter,  and 
4,300  feet  is  6  inches  in  diameter.  The  bottom  of  the  tank  is  111  feet 
above  the  well  platform.  The  lift  or  head  at  any  time  is,  then,  the 
distance  from  the  well  to  the  well  platform  and  111  feet  plus  the 
amount  registered  on  the  gage  on  the  tank.  The  mean  lift  when 
the  test  was  made  was  135  feet.  The  cylinder  capacity  is  2.4  quarts, 
the  measured  discharge  per  double  stroke  4.5  quarts.  The  mean 
temperature  was  90°  F.,  the  mean  barometric  pressure  28.9  inches. 
The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  48 — 30-foot  wooden  Halliday. 
[Load  per  stroke,  1,265  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles 

6 

6 

6  7 

0.23 

12  miles 

15 

15 

16  9 

0  58 

16  miles  

20 

20 

22.5 

0.77 

20  miles 

24 

24 

27  0 

0  92 

25  miles        .     . 

28 

28 

31.  5 

1.07 

This  windmill  and  pump  had  been  in  use  about  ten  years.  It  fur- 
•nishes  enough  water  during  nine  months  in  the  year,  but  during  the 
months  of  July  and  August  and  part  of  June  and  September  a  steam 
engine  is  at  times  employed  to  work  the  pump.  The  cost  of  repairs 
to  the  mill  and  pump  has  been  from  $50  to  $60  a  year.  The  number 
of  strokes  per  minute  for  different  wind  velocities  is  shown  in  fig.  27. 

This  is  the  largest  windmill  pumping  outfit  that  we  have  tested. 
It  is  interesting  to  compare  its  power  with  that  of  the  smaller  wooden 
mills  and  with  that  of  the  steel  mills. 

Mill  No.  51. — This  is  an  8-foot  Monitor  steel  pumping  mill  on  a  30- 
foot  steel  tower  (see  fig.  29).  The  wind  wheel  has  18  curved  sails, 
each  31|  by  13  by  5  inches,  set  at  an  angle  of  35°  with  the  plane  of 


62  THE    WINDMILL 

the  wheel.  The  well  is  a  dug  well;  depth  to  water,  18|  feet.  The 
water  is  used  for  stock.  The  pump  has  a  3-inch  cylinder,  6  inches 
stroke,  and  1^-inch  suction  and  discharge  pipes.  The  cylinder  is  1 
foot  above  -the  lower  end  of  the  suction  pipe,  and  is  always  under 
water.  A  peculiarity  of  this  mill  is  that  the  downstroke  of  the  pump 


FIG.  39.— Working  parts  of  mill  No.  51— 8-foot  Monitor. 

is  made  in  less  time  than  the  upstroke.  The  mill  is  back-geared, 
35  to  13,  13  of  the  cogs  being  passed  over  on  the  downstroke  and  22 
on  the  upstroke.  This  arrangement  makes  the  mill  run  easily  and 
prolongs  its  usefulness.  The  wind  wheel  is  held  in  the  wind  by  the 
weight  of  the  tail ;  there  is  no  spring.  The  li f t  was  25  feet,  the  discharge 
per  stroke  0.7  quart.  The  mean  temperature  was  84°  F.,  the  mean 


MURPHY.] 


RESULTS    OF    TESTS    OF    PUMPI 


barometric  pressure  27.8  inches.     The  results 
lows: 

Results  of  tests  of  mill  No.'  51- -8-foot  steel  Monitor 

[Load  per  stroke,  36.5  foot-pounds.] 


Wind  velocity  per  hour. 

Revolutions 
of  wind  wheel 
per  minute. 

Strokes  of 
pump  per 
minute. 

Gallons 
pumped  per 
minute. 

Useful  horse- 
power. 

8  miles                 .  

27 

10 

1.7 

0.011 

12  miles 

56 

21 

3.7 

0  023 

16  miles 

81 

30 

5.2 

0.034 

20  miles      

91 

34 

6.0 

0.037 

When  the  mill  was  running  uncoupled  from  the  pump,  the  pump 
rod  made  24  strokes  per  minute  in  a  12-mile  wind,  i.  e.,  the  pump 
load  of  36. 5  foot-pounds  per  stroke  reduced  the  number  of  the  strokes 
of  the  pump  rod  from  24  to  21. 

For  the  purpose  of  ready  comparison  the  principal  results  of  these 
tests  of  pumping  mills  have  been  tabulated.  (See  table  on  p.  64.) 

DISCUSSION   OF   RESULTS   OF   TESTS. 

In  this  discussion  of  the  results  of  the  tests  of  these  pumping  mills 
we  wish  to  call  attention  to  the  principal  facts  shown  by  them.  The 
explanation  of  some  of  the  points  is  not  easy.  The  useful  work  which 
a  windmill  will  do  at  a  given  wind  velocity  depends  on  several  factors, 
and  it  is  difficult  to  measure  or  even  estimate  the  value  of  each.  If 
the  mills  could  be  tested  under  conditions  easily  controlled  by  the 
experimenter,  the  problem  would  be  greatly  simplified ;  but  each  mill 
is  tested  under  its  own  conditions  of  pump,  well,  wind  exposure,  and 
atmosphere.  A  comparison  of  the  results  of  the  tests  of  pumping 
mills  with  the  results  of  the  tests  of  power  mills  throws  much  light  on 
some  of  the  facts  (see  Part  II,  pages  107  to  109,  inclusive).  A  fact 
very  evident  from  the  following  table  is  that  the  useful  work  done 
by  windmills  in  pumping  water  is  small.  Only  one  mill,  the  largest 
(No.  48),  is  doing  1  horsepower  of  useful  work  in  a  25-mile  wind. 
The  best  12-foot  mill  is  doing  less  than  0.64  horsepower  and  the  best 
8-foot  mill  less  than  0.12  horsepower  in  a  25-mile  wind. 


64 


THE    WINDMILL. 


[NO.  41. 


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dddddd    Idddddddc 


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MURPHY.]  RESULTS    OF    TESTS    OF    PUMPING    MILLS.  65 

From  the  foregoing  table  it  will  be  seen  that  mills  of  the  same  size 
differ  very  much  in  the  amount  of  useful  work,  and  that  some  of  the 
larger  mills  are  doing  very  little  more  work  than  some  of  the  smaller 
ones.  Nos.  4  and  18,  for  example,  are  the  same  size  and  make  (the 
wells,  however,  are  very  different),  but  the  latter  is  doing  three  or 
four  times  more  work  than  the  former.  The  12-foot  mill,  No.  11,  is 
doing  nearly  as  much  useful  work  as  the  16-foot  mill,  No.  9,  and  three 
or  four  times  more  work  than  the  14-foot  mill,  No.  12,  while  it  is  doing 
300  per  cent  more  work  than  No.  21.  The  lo^-foot  Jumbo  will  prob- 
ably do  little  more  work  during  the  season  than  a  good  8-foot  mill. 

RELATION   BETWEEN   WIND   VELOCITY   AND   STROKES   OF   PUMP. 

Figs.  6,  10,  11,  12,  13,  15,  17,  18,  19,  and  21  show  graphically  the 
relation  between  the  wind  velocity  (in  miles  per  hour)  and  the  strokes 
of  the  pump.  The  curves,  as  will  be  noted,  differ  considerably;  but 
with  the  exception  of  fig.  19,  for  mill  No.  20,  they  agree  in  that  they 
rise  rapidly,  reaching  the  highest  point  at  wind  velocities  of  from  13 
to  19  miles.  From  that  point  they  descend  slowly.  They  differ  much 
in  the  position  of  the  beginning  of  the  curve,  or  the  velocity  required 
to  start  the  mill.  Some  will  run  in  an  8-mile  wind,  while  others  require 
a  10-mile  or  a  12-mile  wind  to  start  them.  Some  rise  less  rapidly  than 
others,  a  notable  case  being  mill  No.  11.  Some  descend  much  more 
rapidly  than  others  after  reaching  the  highest  point.  This  is  especially 
true  of  the  8-foot  Ideals.  Mill  No.  20  required  a  14-mile  wind  to  start 
it,  and  does  not  appear  to  have  a  maximum.  The  shape  of  the  curve, 
especially  the  position  of  its  initial  point,  is  due  to  the  load  on  the 
pump,  or  the  number  of  foot-pounds  per  stroke.  An  increase  in  the 
load  moves  the  curve  to  the  right  and  raises  it  higher.  This  will  be 
more  clearly  shown  in  Part  II  (see  discussion  on  12-foot  power  mill  No. 
27,  pp.  86-89).  The  height  and  position  of  the  highest  point  depend 
on  the  tension  of  the  spring,  or  the  weight  which  holds  the  mill  in  the 
wind.  The  greater  the  tension  the  higher  the  summit  and  the  farther 
it  is  to  the  right;  the  less  the  tension  in  the  spring  the  steeper  the 
descent  from  the  highest  point.  The  gearing — i.  e.,  the  mechanism 
which  causes  the  pump  to  make  a  stroke  to  each  revolution  of  the 
wheel,  or  a  stroke  every  second  or  third  revolution  only — modifies  the 
curve.  In  mills  with  a  direct  stroke  the  curve  is  much  higher  and 
is  farther  to  the  right  than  in  back-geared  mills,  as  shown  by  a  com- 
parison of  the  curves  of  mills  Nos.  3  and  21,  shown  in  figs.  10  and  21. 

USEFUL  WORK   OF   PUMPING  MILLS. 

The  relation  between  wind  velocity  and  horsepower  is  shown  graph- 
ically, for  five  12-foot  mills  in  fig.  30,  and  for  four  8-foot  mills  in  fig. 
31.  Examining  the  five  curves  of  fig.  30,  we  see  that  No.  11,  the  one 
which  gives  the  greatest  horsepower,  has  the  heaviest  load  and 
requires  the  greatest  wind  velocity  to  start  it.  No.  2  has  about 
IRK  41—01 5 


66 


THE    WINDMILL. 


[NO.  41. 


five-eighths  of  the  load  of  No.  11,  does  less  work,  and  requires  about 
the  same  wind  velocity  to  start  it.  No.  3  has  a  lighter  load  than  No. 
2,  and  will  start  in  a  wind  of  about  7  miles  an  hour.  No.  19  has  a 
little  heavier  load  than  No.  3,  and  does  much  less  work  at  all  veloci- 
ties. The  latter  requires  a  9-mile  or  a  10-mile  wind  to  start  it,  while 
the  former  will  start  in  a  7-mile  or  an  8-mile  wind.  No.  21  is  doing 
the  least  work  of  the  five,  and  requires  about  an  11-mile  wind  to  start 
it.  It  is  a  wooden  mill  working  direct  stroke,  while  the  others  are 
steel  mills  and  back-geared. 


10 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 
15  20 


.00 


.4d 


.20 


.10 


pI(;.  30. _ Diagram  showing  relation  between  horsepower  and  wind  velocity  for  five  12-foot  mills. 

It  must  be  understood  that  in  this  comparison  no  correction  or 
allowance  is  made  for  the  difference  in  temperature  and  barometric 
pressure,  nor  for  the  fact  that  in  the  case  of  Nos.  11  and  19  the  Dumps 
are  on  well  points,  while  in  the  others  they  are  in  open  wells. 

It  will  be  seen  that  none  of  the  curves  in  fig.  30  reach  a  maximum 
below  30  miles  an  hour.  They  do,  however,  for  some  higher  veloci- 
ties, since  the  work  per  stroke  of  pump  is  nearly  constant  for  each 
pump  for  all  velocities,  though  not  the  same  for  one  pump  as  for 
another.  The  curves  also  give  the  relation  between  wind  velocity  and 
the  number  of  strokes  of  pump  per  minute. 

In  fig.  31  the  curve  for  No.  18  is  seen  to  reach  a  maximum  at  about 
25  miles  an  hour.  The  others  reach  their  maximum  points  atveloci- 


MURPHY.] 


RESULTS    OF    TESTS    OF    PUMPING    MILLS. 


67 


ties  of  about  30  miles  an  hour.  These  maximum  points  are  points  of 
greatest  speed,  and  are  produced  by  a  reduction  of  wind  area,  the  wind 
wheel  turning  out  of  the  wind.  This  make  of  mill  is  seen  to  "gov- 
ern," or  turn  out  of  the  wind,  at  a  lower  velocity  than  other  makes. 

Comparing  the  curves  in  fig.  31,  we  see  that  the  pump  doing  the 
most  work  at  high  wind  velocities  is  No.  5,  which  is  also  the  one 
most  heavily  loaded.  The  principal  differences  between  Nos.  4  and 
18,  the  pumps  doing  the  most  and  the  least  work  for  velocities  less 
than  22  miles  an  hour,  are  in  the  load  and  the  well.  No.  4  has  five- 
ninths  of  the  load  of  No.  18,  and  is  on  a  well  point.  The  two  pumps 
doing  the  least  work  are  on  well  points. 


10 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 
15  20 


25 


.10 


.  08 


.06 


.04 


.02 


FIG.  31. — Diagram    showing  relation  between  horsepower  and  wind  velocity  for  four  8-foot 

mills. 

Mill  No.  25  is  used  to  pump  water  for  stock.  Comparing  it  with, 
say,  No.  5,  we  find  that  its  load  is  about  five-ninths  as  great,  and  that 
it  is  doing  about  one-tenth  as  much  work  as  the  latter.  It  will  start 
with  a  wind  velocity  of  about  6  miles  an  hour,  while  the  latter  requires 
a  wind  velocity  of  about  8.5  miles  an  hour. 

It  is  interesting  to  compare  the  results  of  Nos.  35  and  36.  The 
former  is  an  8-foot  back-geared  steel  mill,  heavily  loaded ;  the  latter  is 
a  22.5-foot  direct-stroke  mill,  lightly  loaded.  The  wind  exposure  of 
both  is  very  good.  The  discharge  per  stroke  of  No.  35  is  1.1  quarts, 
that  of  No.  36  about  3  quarts.  The  lift  of  the  former  is  58  feet,  the  lift 
of  the  latter  39  feet.  The  load  per  stroke  of  the  former  is  133  foot- 
pounds, that  of  the  latter  248  foot-pounds.  No.  35  starts  in  about  a 


68 


THE    WINDMILL. 


[NO.  41. 


9-mile  wind,  No.  36  in  a  6-mile  wind.  In  an  8-mile  wind  the  former 
is  doing  no  work,  the  latter  is  making  4.8  strokes  per  minute;  but  in 
a  12-mile  wind  the  former  is  making  19  strokes  per  minute,  the  latter 
only  12;  for  all  higher  velocities  the  former  is  making  60  per  cent 
more  strokes  than  the  latter.  For  wind  velocities  above  12  miles  an 
hour  the  horsepower  of  the  22.5-foot  mill  is  only  from  7  to  17  percent 
greater  than  that  of  the  8-foot  mill.  The  difference  is  really  not  so 
great  as  this,  as  the  actual  discharge  is  not  so  great  as  we  have 
supposed. 

PRESSURE-TANK   SYSTEM. 

Mill  No.  37  is  of  special  interest,  in  that  the  water  is  forced  into  a 
pressure  tank  instead  of  into  an  elevated  tank.  This  system  is  said 
to  be  in  use  to  some  extent  in  the  Eastern  States,  and  is  just  coming 
into  use  in  the  West.  The  advantage  claimed  for  it  is  that  the  tank 
can  be  placed  in  a  cellar  or  under  ground,  where  it  will  not  freeze, 
instead  of  on  an  elevated  structure.  A  hydraulic  regulator  is  used, 
which  causes  the  mill  to  turn  out  of  the  wind  when  the  pressure  in 
the  tank  reaches  a'  certain  amount.  In  this  case  the  tank,  which  is 
located  in  a  cellar,  is  2  feet  in  diameter  and  9.5  feet  long;  it  is  about 
170  feet  from  the  well  and  about  43  feet  above  the  surface  of  the 
water  in  the  well.  The  discharge  (1.05  quarts  per  stroke)  is  pumped 
into  the  tank,  then  forced  by  the  confined  air  through  a  1-inch  iron 
pipe  to  the  hydrants,  then  through  a  line  of  rubber  hose  to  the  desired 
point.  The  pressure  in  the  tank  diminishes  with  the  reduction  in  the 
quantity  of  water  in  it.  For  different  volumes  of  air  it  is  as  follows : 

Pressures  in  tank  for  different  volumes  of  air. 


Air  volume. 

Pressure. 

Barrels. 
11.1          

Pounds. 
0 

5.6 

14.7 

3.7 

29.4 

2.8 

44.1 

2.2        

58.8 

1.9 

73.5 

1.6 

88.2 

1.4                          .     .. 

103.0 

The  objection  to  this  system  can  easily  be  seen  from  this  table. 
When  the  pressure  is  103  pounds  per  square  inch  the  withdrawal 
of  0.2  barrel  of  water  from  the  tank  lowers  the  pressure  to  88.2 
pounds,  and  the  withdrawal  of  an  additional  0.3  barrel  lowers  the 
pressure  to  73.5  pounds;  in  other  words,  the  withdrawal  of  a  half  bar- 
rel of  water  when  the  pressure  is  103  pounds  lowers  the  pressure  30 
pounds.  We  found,  on  trial,  that  when  the  pump  was  not  working 
(no  wind),  and  the  pressure  was  at  59  pounds,  one  hose  stream  through 
a  ^-inch  nozzle  reduced  the  pressure  to  50  pounds  in  one  minute  and 


MURPHY.]  RESULTS    OF    TESTS    OF    PUMPING    MILLS.  69 

to  45  pounds  in  two  minutes.  In  seven  minutes  it  fell  to  30  pounds, 
and  in  seventeen  minutes  from  the.  time  of  opening  the  cock  it  fell  to 
20  pounds.  In  a  20-mile  to  30-mile  wind,  and  with  one  hose  stream 
running,  the  pump  kept  the  pressure  in  the  tank  at  about  30  pounds. 
Where  only  a  small  amount  of  water  is  needed  at  a  time  this  system 
will  probably  give  satisfaction.  By  the  use  of  a  larger  tank  more 
water  can  be  obtained  for  a  given  reduction  of  pressure. 

It  will  be  noticed  that  this  is  the  same  size  and  make  of  mill  as  No. 
2,  but  that  it  is  altogether  different  from  No.  41.  No.  2  is  more  heavily 
loaded  than  No.  37.  The  heaviest  load  on  No.  37  is  472  foot-pounds 
per  stroke  of  pump;  the  heaviest  load  on  No.  2  is  536  foot-pounds  per 
stroke.  No.  2  is  doing  the  most  useful  work,  but  the  hydraulic  regu- , 
lator  acts  on  No.  37  to  turn  it  partly  out  of  the  wind  for  the  load  43 
plus  75  pounds.  No.  41  is  doing  very  little  work,  but  it  is  lightly 
loaded  and  working  direct  stroke. 

COMPARISON  OF   THREE   PUMPING   AERMOTORS. 

Comparing  the  16-foot  Aermotor  No.  9,  the  12-foot  Aermotor  No.  3, 
and  the  8-foot  Aermotor  No.  5,  a  diagram  was  plotted  of  the  horse- 
power of  these  three  mills,  drawn  to  the  same  scale.  They  were  found 
to  start  at  about  the  same  wind  velocity,  viz,  7  miles  an  hour,  which 
indicates  about  the  same  total  load.  In  a  25-mile  wind  the  8-foot 
mill  was  found  to  be  yielding  0.1  horsepower,  the  12-foot  mill  0.29 
horsepower,  and  the  16-foot  mill  0.6  horsepower.  In  other  words, 
the  12-foot  mill  was  doing  about  three  times  and  the  16-foot  mill 
about  six  times  more  work  than  the  8-foot  mill.  The  conclusion  can 
not  be  drawn  from  this  that  the  powers  of  the  mills  are  to  each  other 
in  these  ratios,  since  the  pump  efficiencies  are  not  the  same. 

USEFUL   WORK   OF   TWO   PUMPING   MILLS   IN   A   GIVEN   TIME. 

The  useful  work  which  two  pumping  mills  of  the  same  wind  area, 
exposure,  pump  efficiency,  and  general  character  will  do  depends 
on  the  load  on  the  mill  and  the  wind  velocity.  If  the  mill  is  heavily 
loaded  it  will  do  more  work  at  wind  velocities  of  12  or  more  miles 
an  hour  and  less  work  at  lower  velocities  than  one  of  lighter  load. 
The  useful  work  done  in  a  given  time  is  the  product  of  the  work 
done  per  hour  at  the  mean  velocity  multiplied  by  the  number  of 
hours.  If  the  mean  velocity  at  a  given  place  is  low,  the  mill  load 
must  be  less  for  maximum  work  than  that  at  a  place  where  the  mean 
velocity  is  higher.  To  illustrate  this  fact,  we  will  use  the  results  of 
the  tests  of  two  12-foot  pumping  mills — No.  11,  heavily  loaded  and 
giving  a  greater  horsepower  at  high  wind  velocities  than  any  other 
mill  tested,  and  No.  3,  giving  the  greatest  power  at  low  velocities. 
The  useful  work  per  stroke  of  pump  is  844  foot-pounds  for  No.  11 
and  415  foot-pounds  for  No.  3.  The  useless  work  of  the  former  is 
greater  than  that  of  the  latter,  since  the  pump  of  the  former  is  on 


70 


THE    WINDMILL. 


[NO.  41. 


two  well  points,  while  the  pump  of  the  latter  is  in  an  open  well.  The 
relation  between  the  horsepower  and  the  wind  velocity  is  shown  in 
fig.  30.  The  curves  are  seen  to  cross  each  other  at  a  wind  velocity  of 
12.5  miles  an  hour.  For  less  velocities  than  that  No.  3  is  doing  more 
work  per  hour  than  No.  11,  and  for  greater  velocities  No.  11  is  doing 
more  work  than  No.  3.  If  the  velocity  were,  say,  not  more  than  13 
miles  an  hour,  it  is  very  evident  that  mill  No.  3  would  do  more  work 
in  a  given  time  than  mill  No.  11. 

There  is  no  record  of  wind  movement  at  Garden,  Kansas  (where  most 
of  these  tests  of  pumping  mills  were  made),  for  any  considerable  length 
of  time.  There  is  one,  however,  for  Dodge,  50  miles  east  of  Garden, 
kept  by  the  United  States  Weather  Bureau,  which  may  be  used  for 
this  purpose.  The  following  table  gives  the  number  of  hours  per 
month  for  the  six  months  April  to  September^  for  the  years  1889  to 
1895,  inclusive,  when  the  wind  movement  was,  respectively,  0  to  5,  6  to 
10,  11  to  15,  16  to  20,  21  to  25.  26  to  30,  31  and  more  miles  per  hour. 

Mean  wind  movement  at  Dodge,  Kansas,  for  the  seven  years  1889  to  1895. 


Month. 

0-5 
miles. 

6-10 
miles. 

11-15 
miles. 

16-20 
miles. 

21-25 
miles. 

26-30 
miles. 

31  and 
greater. 

April    . 

Hours. 
116 

Hours. 
175 

Hours. 
157 

Hours. 
113 

Hours. 
76 

Hours. 
43 

Hours. 
40 

May 

116 

195 

168 

120 

74 

39 

32 

June 

120 

187 

139 

111 

86 

49 

28 

July.   
August 

144 

178 

218 
230 

176 
152 

117 
99 

57 

62 

23 

18 

9 
5 

September  .  ..  . 

166 

182 

152 

93 

75 

34 

18 

Mean  -  .  . 

140 

198 

157 

109 

72  - 

34 

22 

It  will  be  seen  from  this  table  that  the  wind  velocity  at  Dodge  is  5 
miles  or  less  per  hour  for  140  hours  per  month.  During  this  time 
neither  of  these  mills  (Nos.  3  and  11)  will  do  any  work,  as  neither 
will  start  in  a  5-mile  wind. 

The  velocity  is  from  6  to  10  miles  an  hour  for  198  hours  a  month. 
Mill  No.  3  will  start  in  about  a  7-mile  wind,  and  hence  will  run  about 
four-fifths  of  this  time,  or  158  hours.  No.  11  requires  11.5  miles  of 
wind  to  start  it,  and  will  do  no  work  during  this  time. 

The  velocity  is  11  to  15  miles  an  hour  for  157  hours  during  the  month. 
No.  3  will  work  all  of  this  time,  and  No.  11  about  nine-tenths  of  the 
time,  or  141  hours. 

Both  mills  will  run  at  all  higher  velocities.  At  Dodge,  mill  No.  3 
will  run  (if  in  the  wind)  about  75  per  cent  of  the  time,  and  No.  11 
about  51  per  cent  of  the  time.  For  convenience,  these  results  have 
been  tabulated. 


MURPHY.]  RESULTS    OF   TESTS    OF    PUMPING    MILLS. 

Comparative  results  of  tests  of  two  pumping  mills. 


71 


Mill  No.  3.    ' 

B 

lill  No.  11 

miles  per  hour. 

Hours  per 
month. 

Horse- 
power. 

Product. 

Hours  per 
month. 

Horse- 
power. 

Product, 

6  to  10 

158 

0.067 

10.6 

0 

0.00 

0.0 

11  to  15  ..     .. 

157 

0.168 

26.4 

141 

0.19 

26.8 

16  to  20  

109 

0.230 

25.1 

109 

0.40 

43.6 

21  to  25 

72 

0.277 

19.9 

72 

0.56 

40.3 

26  to  30 

34 

0.  308 

10.5 

34 

0.63 

21.4 

31  and  greater 

22 

0.320 

7.0 

22 

0.64 

14.1 

Total 

99.5 

146.2 

The  second  and  fifth  columns  in  this  table  give  the  number  of  hours 
during  the  mean  month  that  each  mill  will  run  with  a  wind  velocity 
of  from  6  to  10  miles  an  hour.  The  third  and  sixth  columns  give  the 
horsepower  for  the  mean  velocity;  for  example,  0.168  is  the  horse- 
power for  No.  3  at  a  wind  velocity  of  13  miles  an  hour,  and  0.19  is  the 
horsepower  for  No.  11  at  the  same  velocity.  The  fourth  and  seventh 
columns  (the  product  of  the  number  of  hours  and  the  horsepower) 
give  the  horsepower  that  each  mill  will  yield  during  the  month.  It 
will  be  seen  that  No,  11  is  doing  31  per  cent  more  useful  work  than 
No.  3.  If  this  comparison  be  made  for  the  month  of  August,  it  will 
be  found  that  No.  11  will  do  26  per  cent  more  useful  work  during  that 
month  than  No.  3. 

PROPER  LOAD. 

It  will  be  seen  from  what  has  just  preceded,  that  the  useful  power 
of  a  pumping  mill  depends  to  a  great  extent  on  its  load.  If  the  water 
is  needed  constantly  and  there  is  little  or  no  storage,  as  in  the  case  of 
water  for  stock,  the  mill  must  be  lightly  loaded,  and  the  useful  work 
it  will  do  is  small.  If,  however,  there  is  plenty  of  storage,  the  mill 
will  pump  the  largest  amount  of  water  if  heavily  loaded.  If  there 
were  some  automatic  device  for  increasing  the  load  on  the  mill  as  the 
wind  velocity  increases,  the  problem  of  proper  load  would  be  solved. 
But  such  a  device  seems  difficult  to  construct. 

The  following  table  gives  data  for  back-geared  steel  irrigating  mill 
and  good  pumps  for  use  in  the  semiarid  regions  of  the  West,  especially 
for  Kansas  and  Nebraska. 

Data  regarding  mills  and  pumps  for  use  in  semiarid  regions. 


Diam- 
eter of 
mill. 

Load 
per 
stroke. 

Quantity 
deliv- 
ered pei- 
stroke. 

Lift. 

Cylin- 
der ca- 
pacity. 

Starting 
wind 
velocity 
(  pel- 
hour). 

Speed 
per  min- 
ute in 
20-  mile 
wind. 

Dis- 
charge 
per 
hour. 

Dis- 
charge 
per  24 
hours. 

Feet. 
8 
12 
16 

Ft.-lbs. 
125 
600 
1,100 

Quarts. 
2.0 
9.6 
17.6 

Feet. 
30 
30 

30 

Inches. 

4.5x  8 
8x12 
9x16 

Miles. 
9 
8  to  9 
7  to  8 

Strokes. 
27 
30 
16 

Gallons. 
810 
2,  880 
4,224 

Acre  -ft. 
0.059 
0.  212 
0.311 

72  THE    WINDMILL.  [NO.  41. 

For  half  this  lift,  or  15  feet,  the  cylinder  capacity  should  be  nearly 
doubled,  and  for  double  the  lift  the  cylinder  capacity  should  be  about 
half  that  given  in  the  table. 

In  Part  II  of  this  paper,  published  as  Water- Supply  and  Irrigation 
Paper  No.  42,  will  be  found  a  discussion  of  the  writer's  experiments 
with  power  mills,  a  comparison  of  pumping  mills  with  power  mills,  a 
discussion  of  the  effect  of  tension  of  spring  on  the  horsepower  of 
mills,  a  mathematical  discussion  of  the  tests  of  two  Aermotors,  a  dis- 
cussion of  the  action  of  air  on  the  sail  of  an  Aermotor,  a  discussion 
of  the  useful  work  of  two  power  mills  in  a  given  time,  discussions  of 
the  results  of  tests  of  a  Jumbo  mill  and  of  a  Little  Giant  mill,  a  com- 
parison of  the  Little  Giant  and  Jumbo  mills,  a  comparison  of  the 
Little  Giant  mill  and  the  8-foot  Aermotor,  a  discussion  of  the  indi- 
cated and  true  velocities  of  windmills,  a  comparison  of  the  writer's 
experiments  with  those  of  other  experimenters,  and  economic  consid- 
erations. 

[For  index  see  end  of  Part  II,  Water-Supply  Paper  No.  42.] 

O 


CONTENTS. 


Page. 

Experiments  by  writer — Continued 83 

Power  mills 83 

Method  of  testing 84 

Mills  tested 86 

Comparison  of  power  mills 102 

Comparison  of  pumping  mills  with  power  mills 107 

Effect  of  tension  of  spring  on  speed  and  horsepower  of  mill no 

Mathematical  discussion  of  tests  of  two  Aermotors no 

Action  of  air  on  the  sail  of  an  Aermotor 117 

Useful  work  of  two  power  mills  in  a  given  time 118 

Mathematical  discussion  of  tests  of  Jumbo  mill  No.  55 119 

Relation    between   wind    velocity   and   circumference   velocity   of 

•wheel 122 

Mathematical  discussion  of  tests  of  Little  Giant  mill  No.  56 125 

Comparison  of  Little  Giant  and  Jumbo  mills 127 

Comparison  or  Little  Giant  and  8-foot  Aermotor 128 

Indicated  and  true  velocities 131 

Comparison  of  writer's  experiments  with  those  of  others 135 

Economic  considerations 141 

Index  to  Papers  41  and  42 145 


ILLUSTRATIONS. 


Page. 

PLATE  XV.  View  of  mill  No.  44— 16- foot  Aermotor 94 

XVI.  A,  View  of  mill  No.  57— 24-foot  Little  Giant;  B,  View  of  mill 

No.  55— 7.75-foot  Jumbo 120 

FIG.  32.  Working  parts  of  mill  No.  26— 14-foot  Perkins 85 

33.  Working  parts  of  mill  No.  27 — 12-foot  Aermotor 87 

34.  Foot  gear  of  mill  No.  27 .  88 

35.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  27 88 

36.  View  of  mill  No.  28  —16-foot  wooden  Althouse 90 

37.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  28. .....   .  91 

•  38.  Diagram  showing  horsepower  of  mill  No.  28 91 

39.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  29 — 16-foot 

Aermotor _ 92 

40.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  34 —  14-foot 

Junior  Ideal    93 

41.  Diagram  showing  horsepower  of  mill  No.  34 94 

42.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  44 — 16-foot 

Aermotor  94 

43.  Diagram  showing  horsepower  of  mill  No.  44     95 

44.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  49— 221- 

foot  Halliday ..   96 

45.  Diagram  showing  horsepower  of  mill  N  o.  49 96 

46.  View  of  mill  No.  50— 12-foot  Monitor. 97 

47.  Swivel  gearing  of  mill  No.  50 97 

48.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  50 98 

49.  Diagram  showing  horsepower  of  mill  No.  50 . .  98 

50.  View  of  mill  No.  52— 14-foot  Challenge 99 

51.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  52 100 

52.  Diagram  showing  horsepower  of  mill  No.  52 100 

53.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  53 — 12-foot 

Ideal 101 

54.  Diagram  showing  horsepower  of  mill  No.  53 101 

55.  Comparative  diagram  of  revolutions  of  wind  wheels  of  mills  Nos. 

50.53,  and  27  .                                                    . 105 

56.  Comparative  diagram  of  horsepower  of  mills  Nos.  50,  53,  and  27 107 

57.  Diagram  showing  effect  of  tension  of  spring  of  mill  No.  44 — 16-foot 

Aermotor  ... _•_ _.  110 

58.  Sail  of  16-foot  Aermotor 117 

59.  Outer  end  of  sail  of  16-foot  Aermotor. 117 

60.  Inner  end  of  sail  of  16-foot  Aermotor 1 18 

61.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  55— 7.75- 

foot  Jumbo 126 

79 


80  ILLUSTRATIONS. 

Page. 

FIG.  62.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  55 _  121 

63.  Diagram  showing  horsepower  of  mill  No.  55     . .    122 

64.  Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  56— 4.67- 

foot  Little  Giant  ... .  126 

65.  Diagram  showing  horsepower  of  mill  No.  56 .  _ .  _ .  129 

66.  Diagram  showing  action  of  wind  on  sails  of  mill  No.  56. .  _ 130 

67.  Two  views  of  anemometer  and  cups   131 

68.  Diagrammatic  section  of  anemometer  cups 132 

69.  Diagram  showing  horsepower  of  mill  No.  27 — 12-foot  Aermotor 134 

70.  Diagram  showing  horsepower  of  two  16-foot  Aermotors 139 


THE  WINDMILL:  ITS  EFFICIENCY  AND  ECONOMIC  DSR 

FART  II. 


By  EDWARD  CHARLES  MURPHY. 


EXPERIMENTS  BY  WRITER— CONTINUED. 

In  Part  I  of  this  paper,  published  as  Water-Supply  and  Irrigation 
Paper  No.  41,  will  be  found  a  classification  of  windmills,  a  discussion 
of  regulating  devices,  a  synopsis  of  early  experiments  with  windmills, 
and  a  discussion  of  the  writer's  experiments  with  pumping  mills. 
This  part  (II)  of  the  paper  contains  the  results  of  the  writer's  experi- 
ments with  power  mills,  a  comparison  of  pumping  mills  with  power 
mills,  and  discussions  of  various  facts  developed  by  the  tests,  together 
with  a  comparison  of  the  writer's  experiments  with  those  of  other 
experimenters,  and  the  economic  considerations  of  the  subject. 

POWER  MILLS. 

The  power  mill  differs  essentially  from  the  pumping  mill  in  that  the 
latter  gives  a  reciprocating  motion  to  a  pump  piston,  while  the  for- 
mer gives  a  rotary  motion  to  a  vertical  shaft,  and  this,  in  turn,  to  a 
horizontal  shaft,  which  drives  the  grinder  or  other  machine.  The 
mechanism  by  which  this  is  accomplished  in  the  Aermotor  is  shown 
in  figs.  33  and  34.  The  small  plane  cogwheel  makes  three  revolu- 
tions to  one  revolution  of  the  wind  wheel,  and  the  small  beveled  cog- 
wheel makes  two  revolutions  to  one  revolution  of  the  small  plane 
wheel ;  so  that  the  vertical  shaft  makes  six  revolutions  to  one  revolu- 
tion of  the  wind  wheel ;  or,  as  we  say,  the  shaft  is  geared  forward  6 
to  1.  The  two  beveled  cogwheels  of  the  foot  gear  (fig.  34)  change  the 
motion  around  a  vertical  axis  to  a  motion  around  a  horizontal  axis 
without  changing  the  rate  of  speed.  In  fig.  7,  Part  I,  which  shows 
the  pumping  mill,  it  will  be  seen  that  the  large  cogwheel  which  gives 
the  up-and-down  motion  to  the  piston  makes  one  revolution  to  each  3.3 
revolutions  of  the  wind  wheel,  or  that  the  pump  is  geared  back  3.3  to  1 ; 
so  that  the  vertical  shaft  of  a  power  mill  makes  twenty  revolutions  to 
one  stroke  of  a  pump  worked  by  a  pumping  mill  the  wind  wheel  of 
which  is  running  at  the  same  rate  as  that  of  the  power  mill.  The 

83 


84  THE    WINDMILL.  [NO. 42. 

term  "  geared  mill "  is  sometimes  applied  to  power  mills,  but  inappro- 
priately, since  the  pumping  mill  also  is  geared.  The  latter  is  geared 
back,  the  former  is  geared  forward. 

Power  mills  are  heavier  than  pumping  mills.  They  ordinarily  do 
more  work  and  carry  heavier  loads  than  the  latter.  The  load  on  the 
pumping  mill  is  constant  for  all  wind  velocities,  but  it  may  be  varied 
in  the  power  mill.  The  grinder  is  made  so  that  as  the  speed  increases 
the  quantity  of  corn  which  enters  increases,  and  thus  the  load  and 
work  done  are  increased.  The  mill  is  expected  to  do  three  or  four 
kinds  of  work — for  example,  pump  water,  shell  and  grind  corn,  and 
turn  a  grindstone.  In  a  light  wind  the  pump  only  can  be  worked, 
but  as  the  wind  increases  one  after  another  of  the  three  other  machines 
can  be  set  at  work,  and  thus  the  load  be  suited  to  the  velocity  of  the 
wind  and  the  mill  be  made  to  do  the  maximum  amount  of  work.  Power 
mills  are  not  made  smaller  than  12  feet  in  diameter,  for  the  reason 
that  a  small  size  will  not  give  power  enougli  to  be  of  account  except 
for  pumping.  The  ordinary  steel  power  mills  are  12  feet,  14  feet,  and 
16  feet  in  diameter. 

The  power  that  a  windmill  is  capable  of  developing  can  be  deter- 
mined better  from  a  power  mill  than  from  a  pumping  mill,  because 
the  efficiency  of  the  pump — which  may  be  anywhere  from  20  to  85  per 
cent — is  eliminated,  and  because  the  load  on  the  mill  can  be  varied  at 
will,  and  thus  the  effect  of  the  load  on  the  power  of  the  mill  be  deter- 
mined for  different  wind  velocities. 

METHOD   OF  TESTING. 

The  power  was  measured  by  the  use  of  a  Prony  friction  brake  placed 
on  an  iron  pulley  on  the  foot  gear  or  horizontal  shaft.  The  brake 
was  of  wood,  and  had  an  arm  3  or  4  feet  long.  Near  the  end  of  this 
arm  was  fastened  a  spring  balance  reading  to  quarters  of  a  pound. 
By  turning  the  nuts  on  the  brake  the  spring  balance  could  be  made 
to  read  any  desired  amount.  As  the  brake  on  the  pulley  was  tight- 
ened, the  reading  of  the  spring  balance  was  increased  and  the  num- 
ber of  revolutions  of  the  shaft  decreased.  The  brake  is  shown  in  PI. 
XV.  The  speed  of  the  shaft  was  found  in  one  of  three  ways — which- 
ever was  most  convenient.  A  small  electric  device  was  used  when- 
ever it  could  conveniently  be  attached  to  the  wind  wheel.  The  clicks 
of  this  instrument  could  easily  be  counted,  and  gave  the  number  of 
revolutions  of  the  wind  wheel  for  each  half  mile  of  wind  movement. 
A  speed  counter  was  used,  but  did  not  prove  satisfactory.  Whenever 
the  electric  device  could  not  conveniently  be  employed,  the  number 
of  revolutions  of  the  wind  wheel  was  found  by  counting  the  revolu- 
tions of  a  mark  on  the  wind  wheel  as  reflected  in  a  mirror  con- 
veniently placed. 

To  illustrate :  If  u  is  the  number  of  revolutions  per  minute  of  the 
brake  pulley  as  found  from  the  revolutions  of  the  wind  wheel  per 


MUKPHY.] 


WRITER  S    EXPERIMENTS. 


85 


half  mile  of  wind,  L  the  load  in  pounds  as  read  from  the  spring  bal- 
ance, and  B,  the  length  of  the  arm,,  then  the  useful  work,  in  foot- 
pounds per  minute,  is — W  =  2  ?r  Ru  L,  and  the  horsepower  is — H.  P. 
=  2  n  E  u  L  4-  33,000. 

The  number  of  revolutions  per  minute  of  wind  wheel  was  found  for 
each  mill  for  from  two  to  six  different  brake  loads,  for  wind  velocities 
as  small  as  would  keep  the  mill  working  for  the  particular  load  used 


FIG.  32.— Working  parts  of  mill  No.  36— 14-foot  Perkins. 

up  to  about  25  miles  an  hour.  That  is,  the  reading  of  the  spring  bal- 
ance was  kept  as  nearly  constant  as  possible  until  we  had  obtained 
points  and  a  curve  like  that  shown  in  fig.  10.  Then  the  load  was 
changed  and  the  tests  continued  in  the  same  way,  getting  another 
curve.  From  these  curves  the  number  of  revolutions  of  wind  wheel 
per  minute  for  different  loads  and  wind  velocities  was  easily  found, 
as  before  indicated.  These  are  given  in  the  table  of  results  for  each 
mill  tested,  and  in  many  cases  are  also  shown  by  diagram.  The  horse- 


86 


THE    WINDMILL. 


[NO.  42. 


power  of  any  mill  for  different  loads  and  velocities  is  easily  found  by 
the  foregoing  formula.  These  are  given  in  the  tables  of  results  of 
tests,  and  are  also  shown  l>y  diagrams. 

MILLS   TESTED. 

Mill  No.  26. — This  is  a  14-foot  Perkins  steel  power  mill  on  a  40-foot 
steel  tower,  made  by  the  Perkins  Windmill  Company,  of  Mishawaka, 
Indiana.  The  working  parts  are  shown  in  fig.  32.  The  wind  wheel  has 
32  curved  sails,  each  41  by  14.25  by  7.75  inches,  set  at  an  angle  of  31° 
with  the  plane  of  the  wheel.  The  shaft  is  geared  forward  6  to  1. 
The  radius  of  the  brake  pulley  was  5  inches,  the  length  of  brake 
arm  33.5  inches.  This  mill  was  tested  twice.  Between  the  dates  of 
testing  some  repairs  were  made  to  the  shafting,  causing  the  cogwheels 
to  bind  less  tightly.  The  following  figures  are  those  obtained  from 
the  second  test.  The  mill  had  been  in  use  only  about  one  year,  and 
showed  very  poor  workmanship.  The  results  of  the  test  are  as  follows : 

Results  of  test  of  mill  No.  26 — 14-foot  steel  Perkins. 


Load  on 
brake. 

Load 
per 

revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of  wind 
wheel  per  minute  at  given  wind 
velocities  (per  hour). 

Useful  horsepower  at  given  wind 
velocities  (per  hour). 

1 
1 

oo 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

GO 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

Pounds. 
6 

Ft.-lbs. 
645 

16 

31 

48 

0.313 

0.609 

0.937 

Mill  No.  27.— This  is  a  12-foot  Aermotor  on  a  30-foot  steel  tower. 
The  wind  wheel  is  like  that  of  mill  No.  3  (see  pp.  29  to  30,  Part  I). 
The  horizontal  shaft  is  geared  forward  6  to  1.  Fig.  33  shows  the 
working  parts,  and  fig.  34  the  foot  gear.  The  brake  pully  was  9.5 
inches  in  diameter  and  was  fastened  to  the  foot  gear  at  a  in  fig.  34. 
The  brake  arm  was  35.25  inches  in  length.  The  mean  temperature 
during  the  test  was  46°  F.,  and  the  mean  barometric  pressure  28.9 
inches.  The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  27 — 12  foot  Aermotor. 


Load  on 
brake. 

Load 
per 
revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of 
wind   wheel  per  minute 
at  given  wind  velocities 
(per  hour). 

Useful  horsepower  at  given  wind  ve- 
locities (per  hour). 

I 

fj 

co 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

8  miles. 

12  miles. 

li)  miles. 

1 
§ 

1 
1 

& 

Pounds. 
0 
2 
4 
6 

Ft.-lbs. 
0 
222 
444 
886 

30 

1C, 

49 
43 
23 

88 

57 
4S 
12 

75 
70 
86 
60 

87 

81 
77 
72 

0.  089 

0.285 

(i.:1,!).! 

O.UW5 
0.653 

6.458 

(l.-Sltl) 

1.03 

0.  523 
1.02 
1.45 

MURPHY.] 


POWER    MILLS    TESTED. 


87 


The  revolutions  of  wind  wheel  per  minute  for  the  four  brake  loads 
0,  2,  4,  and  6  pounds,  respectively,  are  shown  in  fig.  35.  The  pull 
necessary  to  overcome  the  frictional  resistance  was  found  by  stand- 
ing on  the  platform  of  the  mill  and  slowly  turning  the  wind  wheel 
around  with  a  spring  balance.  This  was  checked  by  winding  a 


FIG.  33.— Working  parts  of  mill  No.  27— 12-1'oot  Aermotor. 

cord  around  the  circumference  of  the  wind  wheel,  and,  standing  on 
the  ground,  moving  the  wheel  when  there  was  no  wind  by  pulling 
on  the  spring  balance  attached  to  the  cord.  A  pull  of  1.25  pounds 
applied  at  the  circumference  was  sufficient  to  overcome  this  resistance 
at  a  low  velocity.  The  work  done  in  overcoming  this  resistance  is 
1. 25  x27rx  0=47.1  foot-pounds  per  revolution.  The  work  done  per 


88 


THE    WINDMILL. 


[NO.  42. 


revolution  of  wind  wheel  per  pound  on  the  brake  arm  is — 27rx35.25x 
(j-r- 12=111  foot-pounds.  The  ratio  of  these  is  47. 1-r- 111 =0.425  pound. 
Hence  a  brake  load  of  0.425  pound  is  equivalent  to  the  friction  load. 

The  effect  of  each  additional  2 
pounds  load  on  the  brake  in  re- 
ducing the  speed  of  the  wheel  at 
different  wind  velocities  is  clearly 
shown  here.  It  is  seen  that  an 
added  load  makes  a  greater  pro- 
portionate reduction  in  the  speed 
when  the  velocity  is  low  than  when 
it  is  high.  Thus,  in  an  8-mile  wind 
the  addition  of  2  pounds  to  the 
load  reduces  the  speed  50  per  cent, 
while  in  a  25-mile  wind  the  same 
load  reduces  the  speed  only  about 
7  per  cent. 

It  will   be   seen   that    for   wind 
velocities  above  a  certain  amount, 

with  the  load  not  too  great,  each  additional  pound  of  load  reduces 
the  speed  of  the  wheel  by  about  the  same  amount.  For  example,  in 
a  25-mile  wind  the  addition  of  2  pounds  changes  the  speed  from  87 
revolutions  to  81  revolutions.  The  addition  of  2  pounds  more  changes 


PIG.  34. -Foot  gear  of  mill  No.  27-12-foot 
Aermotor.  a  indicates  point  where  brake 
pulley  was  attached. 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

10  15  20 


so 


FIG.  35. — Diagram  showing  revolutions  of  wind  wheel  of  mill  No.  27 — 12-foot  Aermotor.  Curve 
marked  o  is  for  no  brake  load;  curve  marked  2  is  for  a  brake  load  of  2  pounds;  curve  marked  4  is 
for  a  brake  load  of  4  pounds;  curve  marked  6  is  for  a  brake  load  of  6  pounds;  curve  PQ  is  speed 
curve  for  maximum  power. 

the  speed  from  81  revolutions  to  77  revolutions.  It  will  be  seen  that 
as  the  load  increases  the  increment  of  wind  velocitj^  necessary  to  start 
the  mill  increases  more  rapidly  than  the  increment  of  loading.  That 
is,  the  0-pound  load  curve  starts  in  about  a  4.5-mile  wind,  the  2-pound 


MURPHY.]  POWER    MILLS    TESTED.  89 

curve  in  about  a  7-mile  wind,  the  4-pound  curve  in  about  a  10,5-mile 
wind,  and  the  6-pound  curve  in  about  a  15. 5-mile  wind.  The  dif- 
ference between  these  starting  velocities  is  constantly  increasing. 
A  diagram  was  platted  showing  the  horsepower  of  this  mill  for  the 
2-pound,  4-pound,  and  6-pound  brake  loads.  The  curves  showed  that 
for  any  brake  load  the  power  of  the  mill  increased  rapidly  as  the  wind 
velocity  increased,  and  that  it  reached  a  maximum  for  some  velocity 
greater  than  30  miles  an  hour.  As  the  load  increased  the  velocity 
required  to  start  the  mill  increased  rapidly  and  the  curve  became 
steeper.  For  a  given  wind  velocity  the  power  increased  rapidly  as 
the  load  increased.  For  a  velocity  of  25  miles  an  hour  the  power 
was  nearly  proportional  to  the  load  for  loads  of  less  than  6  pounds. 
It  showed  that  when  the  velocity  was  less  than  12  miles  an  hour  a 
4-pound  load  was  too  great,  and  when  it  was  less  than  19  miles  an  hour 
a  6-pound  load  was  too  great.  It  showed  also  that  the  efficiency 
decreased  as  the  wind  velocity  for  a  given  load  increased,  and  that  it 
increased  as  the  load  increased.  The  efficiency  for  a  load  of  2  pounds 
and  a  wind  velocity  of  9  miles  an  hour  was  40  per  cent.  At  14  miles 
an  hour  and  with  a  4-pound  load  it  was  36  per  cent.  If  the  load  at  that 
velocity  was  reduced  to  2  pounds,  the  efficiency  was  reduced  to  24  per 
cent.  Finding  the  efficiency  by  using  the  wind  area  (area  of  circle  12 
feet  in  diameter)  instead  of  the  sail  area,  as  is  sometimes  done,  the 
foregoing  efficiency  of  40  per  cent  with  a  2-pound  load  in  a  9-mile 
wind  became  26  per  cent. 

The  results  for  this  mill  will  be  discussed  from  a  mathematical 
point  of  view  further  on. 

Mitt  No.  28. — This  is  a  16-foot  Althouse  wooden  power  mill  manu- 
factured by  Althouse,  Wheeler  &  Company,  of  Waupun,  Wisconsin. 
It  is  shown  in  fig.  36.  The  axis  of  the  wind  wheel  is  32  feet  above 
the  ground  and  15  feet  above  the  roof  of  a  near-by  blacksmith's 
shop.  The  wind  wheel  has  130  sails,  each  48  by  4  by  1.5  inches,  set 
at  an  angle  of  32°  to  the  plane  of  the  wheel.  Two  half  sails  are  miss- 
ing and  two  others  are  slightly  injured,  making  a  loss  of  about  one 
and  a  half  sails.  The  horizontal  shaft,  which  works  a  sheller,  grinder, 
emery  wheel,  and  wood  saw,  is  geared  forward  8.377  to  1.  A  pull  of 
from  7  to  13  pounds  at  a  distance  of  6  feet  from  the  center  was  neces- 
saiy  to  start  the  mill,  showing  it  to  be  a  hard-running  one.  The 
brake  pulley  was  8  inches  in  diameter,  the  brake  arm  3.5  feet  long. 
A  second  visit  to  this  mill  was  necessary  in  order  to  get  results  for 
high  velocities.  During  the  interval  between  the  tests  a  510-pound 
ny  wheel  was  put  on  the  shaft,  which  steadied  the  motion  of  the  mill 
somewhat.  Tlie  owner  is  well  pleased  with  the  action  of  this  balance 
wheel.  Single  measurements  of  the  power  of  this  mill  for  the  same 
load  and  wind  velocity  differ  considerably.  It  is  very  evident  that 
this  mill  is  not  high  enough;  if  it  were  30  or  40  feet  higher  it  would 
IKK  4^—01 2 


90 


THE    WINDMILL. 


[NO.  42. 


give  better  results.  It  is  with  the  aid  of  better  results  obtained  from 
tests  of  other  mills  of  similar  make  that  we  are  able  to  give  tho  results 
in  the  following  table  and  in  the  diagrams. 


, 


ft 


FIG.  36.— View  of  mill  No.  28— 16-foot  wooden  Althouse. 
Results  of  tests  of  mill  No.  2S — Ki-foot  wooden  AltJtonxe. 


- 

Load 

Number  of  revolutions  of  wind 
wheel  per  minute  at  given 
wind  velocities  (per  hour). 

Horsepower  of  mill    at    given  wind 
velocities  (^er  hour). 

Load  oil 
brake. 

per  rev- 
olution 
of  wind 

. 

A 

03 

B 

wheel. 

i 

r2 

| 

I 

I 

i 

1 

s 

I 

1 

a 

i 

a 

a 

1 

a 

a 

a 

g 

00 

M 

s 

8 

K 

CO 

23 

«1 

8 

£ 

Pounds. 

Ft.-lbs. 

0 

0 

13 

23 

30 

36 

40 

U 

437 

20 

27 

31 

36 

0.26 

0  35 

0  40 

0.  40 

G. 

5 

13 

20 

88 

5J 

914 

19 

23 

27 

0.52 

0.  64 

(».  75 

4 

1,462 

8 

13 

15 

0.35 

0.00 

0.67 

Fig.  37  shows  the  number  of  revolutions  prr  minute   of  the  wind 
wheel  of  this  mill  for  the  brake  loads  0,  1.75,  5.75,  and  S.75  pounds, 


MURPHY.] 


POWER   MILLS    TESTED. 


91 


-VELOCITY  OP  WIND   IN  MILKS  PEK  HOUR. 

10  15  20 

40 


Id 


FIG.  37. — Diagram  showing  revolutions  of  wind 
wheel  of  mill  No.  28— 16-foot  wooden  Althouse. 
Curves  marked  0, 1. 75, 5.75, 8.75,  and  grinder  are 
for  brake  loads  of  0,  1.75,  5.75,  and  8.75  pounds, 
respectively,  and  for  grinder  load. 


and  for  grinder  load.  The  curve  for  the  grinder  load  is  a  nearly 
straight  line.  This  is  due  to  the  fact  that  the  grinder  is  constructed 
so  that  as  its  speed  increases  the 
amount  of  corn  it  receives  in- 
creases ;  thus  the  load  increases 
automatically  as  the  wind  veloc- 
ity increases.  By  comparing 
these  speed  curves,  as  they  may 
be  called,  with  those  of  fig.  35, 
for  the  Aermotor,  it  will  be  seen 
that  the  speed  of  the  latter  is 
much  greater  than  that  of  mill 
No.  28. 

Fig.  38  shows  the  horsepower  of 
this  mill  for  three  brake  loads — 
1.75  pounds,  5.75  pounds,  and 
8. 75  pounds.  The  latter  load  is 
too  great  for  the  mill.  By  com- 
paring the  results  for  this  mill 
with  those  for  the  12-foot  Aer- 
motor (fig.  35)  it  will  be  seen 
that  the  latter  mill  is  superior  to  the  16-foot  wooden  mill. 

Mill  No.  29. — This  is  a  16-foot  Aermotor  like  that  shown  in  PI.  XV. 

It  is  manufactured  by  the  Aer- 

OF  WIND  IN  MILES  PER  HOUR.  motor  Company,  of  Chicago, 
25  Illinois.  The  tower  is  of  wood, 
42  feet  to  the  axis  of  the  Avheel. 
The  wind  wheel  has  18  curved 
sails,  each  59  by  25.75  by  10.5 
inches,  set  at  an  angle  of  30°  to 
the  plane  of  the  wheel.  It  is 
used  for  shelling  and  grinding 
corn  and  for  working  a  small 
pump.  The  shafting  is  20  feet 
above  the  ground,  near  the  roof 
of  a  granary.  It  is  geared  for- 
ward 6  to  1,  and  arranged  so 
that  the  pump  makes  1.011 
strokes  to  each  revolution  of  the 
wind  wheel.  The  pump  lifts 
0.022  gallon  per  stroke  a  dis- 
tance of  about  40  feet.  It  has  a 
cylinder  1.5  inches  in  diameter 
and  a  stroke  of  8  inches.  The 
supply  pipe  is  on  a  well  point. 

The  brake  pulley  is  12  inches  in  diameter,  the  brake  arm  3.75  feet  long. 
The  test  was  continued  until  the  shafting  failed.     The  mean  baro- 


FIG.  38. — Diagram  showing  horsepower  of  mill 
No.  28— 16-foot  wooden  Althouse.  Curves 
marked  1.75,  5.75,  and  8.75  show  horsepower  for 
brake  loads  of  1.75,  5.75,  and  8.75  pounds,  respec- 
tively; dotted  curve  HK  shows  maximum 
power. 


92 


THE    WINDMILL. 


[NO.  42. 


metric  pressure  was  27.8  inches,  the  mean  temperature  70°  F.  This 
mill  had  been  in  nearly  constant  use  about  five  years.  It  replaced  a 
22.5-foot  Halliday.  The  owner  claims  that  the  16-foot  steel  mill  does 
more  work  than  the  22.5-foot  Halliday  wooden  mill  did.  The  results 
of  the  tests  are  as  follows : 


Results  of  tests  of  mill  No.  29 — 16-foot  Aermotor. 


Load  on 
brake. 

Load 
per  rev- 
olution 
of  wind 
wheel. 

Nun: 
wh 
vel 

1 
1 

oo 

iber  of  revolutions  of  wind 
eel  per  minute  at  given  wind 
ocities  (per  hour). 

Horsepower  of  mill  at  given  wind 
velocities  (per  hour). 

12  miles. 

16  miles. 

20  miles. 

1 

a 
& 

8  miles. 

12  miles. 

1 
1 

s 

20  miles. 

25  miles. 

Pounds 

P+li 

P+24 

Ft.-lbs. 
212 

487 
629 

20 
11 

35 
30 
25 

0.13 
0.17 

0.23 
0.44 
0.48 

4i 
35 

0.636 
0.714 

VELOCITY  OF  WIND  IN  MILES   PER 
HOUR. 


o 

2   30 


Fig.  39  shows  the  number  of  revolutions  of  the  wind  wheel  for  three 
loads — 212  foot-pounds,    487   foot-pounds,    and    629   foot-pounds. 

Although  these  results  are  incomplete, 
on  account  of  the  failure  of  the  shaft- 
ing, they  are  complete  up  to  a  wind 
velocity  of  15  miles  an  hour,  and  when 
studied  in  connection  with  the  com- 
plete test  of  a  mill  of  the  same  size  and 
make  (No.  44)  it  will  be  seen  that  this 
mill  has  about  the  same  power  for  the 
same  loads  at  any  given  wind  velocity. 
Mill  No.  30.—  This  is  a  16-foot  wooden 
power  mill  known  as  an  Irrigator,  used 
for  lifting  water.  (For  description  see 
pp.  49-50,  Part  I.)  Two  brake  loads  (2 
pounds  and  16  pounds)  were  used  on  an 
arm  2.5  feet  long.  Curves  showing  the 
number  of  revolutions  of  the  wind  \vhcol 
per  minute  for  these  loads  and  the  use- 
ful elevator  load  are  reproduced  in  fig. 
22,  Part  I;  the  horsepowers  for  these 
loads  are  shown  in  fig.  23,  Part  I. 

Mill  No.  31.—  This  is  a  14-foot  Elgin 
wooden  power  mill  used  to  lift  water 
with  a  rotary  (Wonder)    pump.     It  is 
described  on  pages  50  to  51,  Part  I. 
Mill  No.  34. — This  is  a  14- foot  Junior  Ideal  steel  power  mill  manu- 
factured by  the  Stover  Manufacturing  (1onipany,  of  Freeport,  Illinois. 
The  tower  is  of  wood,  41  feet  to  the  axis  of  the  wheel.     The  wheel  has 


A     C 


PKJ.  W.  -Diagram  showing  revolutions 
of  wind  wheel  of  mill  No.  29— 16-foot 
Aermotor.  Curve  AB  is  for  a  load  of 
212  foot-pounds;  CE  is  for  a  load  of 
4«7  foot-pounds;  DF  is  for  a  load  of 
629  foot-pounds. 


MURPHY.] 


POWER    MILLS    TESTED. 


93 


VKLOCITY  OF  WIND  IN   MILES  PER  HOUR. 

10  15  20  25 


41; 


24  curved  sails  in  eight  sections,  regulated  on  the  centrifugal  prin 
ciple.  Each  sail  is  49  by  18 
by  8  inches,  set  at  an  angle  of 
29°  to  the  plane  of  the  wheel. 
This  is  a  sectional  vaneless 
mill.  In  place  of  a  vane  there 
is  M  counterpoise.  It  is  geared 
forward  8  to  1.  The  mill  is 
used  for  shelling  and  grind- 
ing corn  and  elevating.  The 
brake  pulley  is  on  a  line  shaft 
15  or  20  feet  long.  In  a  12- 
mile  wind  the  mill  ground  12 
pounds  quite  fine  for  a  mile  of 
wind,  or  at  the  rate  of  144 
pounds  an  hour.  In  an  18- 
mile  wind  it  ground  26  pounds 
for  a  mile  of  wind,  or  at  the 
rate  of  468  pounds  an  hour. 
The  grinder  was  made  by  the 
Baker  Manufacturing  Com- 
pany, of  Evansville,  Wiscon- 
sin. The  wind  was  unsteady, 
the  temperature  high — 100° 
in  the  shade  at  noon.  The  re- 
sults of  the  tests  are  as  follows : 


10 


FIG.  40.— Diagram  showing  revolutions  of  wind 
wheel  of  mill  No.  34— 14-foot  Junior  Ideal. 
Curves  marked  0,  1,  3£,  and  grinder  are  for 
brake  loads  of  0, 1 ,  and  3.5  pounds,  respectively, 
and  for  grinder  load. 


Results  of  tests  of  mill  No.  34 — 14-foot  steel  Junior  Ideal. 


Load  on 
brake. 

Load  per 
revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of  wind 
wheel  per  minute  at  given  wind 
velocities  (per  hour). 

Horsepower  of  mill  at  given  wind 
velocities  (per  hour). 

3 
a 

CO 

12  miles. 

16  miles. 

20  miles. 

93 
* 
1 
g 

1 

a 

00 

12  miles. 

16  miles. 

1 
1 

25  miles. 

Pounds. 
0 
1 
G. 

Ft.-lbs. 
0 
180 
G. 
631 

20 
13 
4 
0 

34 
29 
19 
0 

44 
40 
32 
24 

53 
49 
39 
32 

58 
55 
47 
40 

0.07 

0.16 

0.22 

0.27 

0.33 

0 

0 

0.46 

0.61 

0.76 

Fig.  40  shows  the  number  of  revolutions  of  the  wind  wheel  per  min- 
ute for  brake  loads  of  0,  1,  and  3.5  pounds,  and  for  the  grinder  load. 
Fig.  41  shows  the  horsepower  for  brake  loads  of  1  and  3.5  pounds. 

Mill  No.  44. — This  is  a  16-foot  Aer motor  on  a  40-foot  steel  tower. 
(See  PL  XV.)  The  working  parts  of  the  mill  are  like  those  shown  in 
fig.  33 ;  the  foot  gear  is  like  that  shown  in  fig.  34.  The  sail  area  is  the 
same  as  that  of  mill  No.  29,  page  91.  The  power  was  measured  with 
a  wooden  brake  having  an  arm  4.67  feet  long,  on  a  10-inch  iron  pulley 
on  the  foot  gear.  Five  brake  loads  were  used — 0,  3,  5,  8,  and  11  pounds, 
respectively.  The  shafting  is  geared  forward  6  to  1. 


94 


THE    WINDMILL 


[NO.  42. 


The  results  of  the  tests  are  as  follows : 

Results  of  tests  of  mill  No.  44 — 16-foot  Aermotor. 


Load  on 
brake. 

Load  per 
revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of  wind 
wheel  per  minute  at  given  wind 
velocities  (per  hour). 

Horsepower  of  mill  at  given  wind 
velocities  (per  hour). 

8  miles. 

12  miles. 

16  miles. 

1 

8 

25  miles. 

1 
oo 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

Pounds. 
0 
3 
5 
8 
11 

Ft.-lbs. 
0 

528 
880 
1,408 
1,936 

23 

38 
28 
13 

48.0 
41.0 
33.5 
16.0 

56 
50 
44 
36 
25 

64.5 
58.5 
53.5 
47.0 
39.5 



0.45 
0.35 

0.66 
0.89 
0.68 

0.80 
1.16 
1.53 
1.47 

0.94 
1.43 
2.01 
2.31 

VELOCITY  OF  WIND  IN   MILES   PEK  HOUR, 
10  15  20 


FIG.  41.— Diagram  showing  horsepower  of  mill 
No.  34-14- f oot  Junior  Ideal.  Curves  marked  3J 
and  1  show  power  for  brake  loads  of  3.5  pounds 
and  1  pound,  respectively;  dotted  curve  IK 
shows  maximum  power. 


Fig.  42  shows  the  number  of 
25  revolutions  per  minute  of  the 
wind  wheel  for  these  brake 
loads.  The  number  on  each 
curve  indicates  the  brake  load 
for  that  curve.  These  curves 
are  seen  to  closely  resemble  the 
corresponding  curves  for  the  12- 
foot  Aermotor  (fig.  35).  The 
16-foot  mill  will  be  seen  to  start, 
with  no  load,  in  about  a  4. 5-mile 
wind — the  same  as  the  12-foot 
Aermotor.  Fig.  43  shows  the 
horsepower  of  this  mill  for  loads 
of  3,  5,  8,  and  11  pounds,  respec- 
tively. The  curves  for  this  mill 
closely  resemble  those  of  the 
12-foot  Aermotor.  The  curves 


VELOCITY  OF  WIND   IN  MILES  PER  HOUR. 

]()  15  20  25 


of  the  latter  were  platted,  but  the  diagram  is  not  reproduced  because 
of  lack  of  space.  It  will  be 
shown  further  on  that  these 
load  curves  are  parabolas, 
and  hence  that  the  power 
increases  as  the  square  root 
of  the  wind  velocity.  It  will 
be  shown  also  that  the  curve 
of  maximum  power  is  a  para- 
bola, that  the  load  for  it 
increases  nearly  as  the  first 
power  of  the  wind  velocity, 
and  that  the  speed  of  Ihr 
wheel  increases  also  as  the 

,  PIG.  42.— Diagram  showing  revolutions  of  wind  wheel 

first  power  Of  the  Wind  Ve-  of  mill  No.  44— 16-foot  Aermotor.  Curves  marked  0, 

,  ..  3,  5,  8,  and  11  are  for  brake  loads  of  0,3  pounds,  5 

lOClty.  pounds,  8  pounds,  and  11  pounds,  respectively;  curve 

n/T'n     \r         in        rni  •        •  ''V  is  *P<'f<l  of  wheel  for  maximum  load; 

Mill    No.    49.  —  IhlS    is    a  curee formaximum  power. 


U.   S.   GEOLOGICAL  SURVEY 


WATER-SUPPLY   PAPFR  NO.   42       PL.    XV 


VIEW   OF   MILL  NO.  44 — 16-FOOT  AERMOTOR. 


MURPHY.] 


POWEE   MILLS    TESTED. 


95 


VELOCITY  OF  WIND     IN   MILES  PER  HOUR. 
10  15  20  25 


22.5-foot  Halliday  wooden  power  mill  on  a  43*-foot  wooden  tower. 
The  sail  area  is  in  two  con- 
centric rings,  the  outer  ring 
having  144  sails,  the  inner 
ring  100  sails,  each  43  by  4.5 
by  3.5  inches,  set  at  an 
angle  of  25°  to  the  plane 
of  the  wheel.  The  upper 
gearing  has  a  ratio  of  50  to 
14,  the  lower  gearing  a  ratio 
of  53  to  26,  so  that  the 
horizontal  shaft  is  geared 
forward  7.28  to  1.  The 
brake  pulley  is  8  inches  in 
diameter,  the  brake  arm  4. 75 
feet  long.  The  mean  tem- 
perature was  82°  F.,  the 
mean  barometric  pressure 
28.7  inches.  The  mill  is 
used  for  shelling  and 
grinding  corn.  Four  brake 
loads  (0,  1.5,  5,  and  9 
pounds,  respectively)  were 
used,  also  the  grinder  load. 


l.( 


0.  f, 


FIG.  43.— Diagram  showing  horsepower  of  mill  No.  44— 
16-foot  Aermotor.  Curves  marked  3, 5, 8,  and  11  show 
power  for  brake  loads  of  3, 5, 8,  and  11  pounds,  respec- 
tively; dotted  curve  DK  shows  maximum  power. 


The  results  of  the  tests  are  as  follows : 


Results  of  tests  of  mitt  No.  49— 22.5-foot  wooden  Halliday. 


Load 
on 
brake. 

Load  per 
revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of  wind 
wheel  per  minute  at   given 
wind  velocities  (per  hour). 

Horsepower  at  given  wind  velocities 
(per  hour). 

CO 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

8  miles. 

12  miles. 

1 
1 
S 

1 
1 

8 

£ 

Pounds. 
0 
1.5 
5.0 
G. 
9.0 

Ft.-lbs. 
0 
326 

1,087 

11 

6 

20 
16 
11 
8 
2 

25 
22 
18 
16 
10 

30 
26 
22 
22 
15 

32 
30 
26 

0.059 

0.163 
0.342 

0.217 
0.593 

0.257 
0.724 

6.296 
0.856 

1,956 



19 

0.118 

0.593 

6.890 

1.126 

Ill  a  13.5-mile  wind  the  mill  ground  20  pounds  of  chop  quite  fine  in 
4.5  minutes.  Fig.  44  shows  the  number  of  revolutions  per  minute  of 
the  wind  wheel  for  the  five  loads.  This  mill  requires  a  5.5-mile  wind 
to  start  it  without  any  load,  and  it  makes  only  32  revolutions  in  a  25- 
mile  wind.  This  is  about  half  as  many  as  are  made  under  the  same 
conditions  by  the  10-foot  mill  No.  44.  Since  the  circumference  of  the 
22. 5-foot  mill  is  1.4  times  greater  than  that  of  the  16-foot  mill,  the  cir- 
cumference velocity  of  the  16-foot  mill  is  44  per  cent  greater  than  that 
of  the  22. 5-1'oot  mill.  The  dotted  curve,  showing  the  speed  of  the  wheel 
for  the  grinder  load,  will  be  seen  to  be  a  nearly  straight  line,  showing  a 


96 


THE    WINDMILL. 


[NO.  42. 


constantly  increasing  load  with  increa  se  of  wind  velocity.  Fig.  45  shows 
the  horsepower  for  three  loads,  also  the  maximum  horsepower.  It  will 
be  seen  that  the  power  is  small  for  so  large  a  mill.  The  shafting  of 
this  mill  is  very  heavy,  and  the  grinder  is  run  by  a  belt  from  the  main 
shaft.  The  mill,  although  on  a  43-foot  tower,  should  be  at  least  20 
feet  higher.  It  will  be  seen  to  be  a  very  poor  mill. 


VELOCITY  OF  WIND   IN  MILES  PER  HOUR. 

10  15  20  35 


VELOCITY  OF  WIND   IN  MILES  PER  HOUR. 

10  15  20  35 


J 

a 

^^^ 

a 

^I0llil»i*0*l~~^ 

g» 

^^**^          ^^ 

.^ 

^^^^ 

A 

o/  —    ^ 

•  — 

fc 

Si.S^ 

.^^~ 

£ 

l/' 

^^ 

EEI   o(i 

^s? 

o  ^ 

/  / 

b/S 

00 

/  / 

^S   ' 

i. 

'  /        s 

r    s 

o 

/ 

/    / 

s             ^, 

| 

// 

,// 

/^ 

o  1() 

/  / 

r 

& 

/  / 

a 

/  / 

« 

/  / 

II    t 

1.3 


K  <U 

O 

CH 

H 

CO 

X 
O 

K  O.t 
Q 
g 


FIG.  44.—  Diagram  showing  revolutions  of 
wind  wheel  of  mill  No.  49—  23.5-foot  wooden 
Halliday.  Curves  marked  0,  1.5,  5,  and  9 
are  for  brake  loads  of  0,  1.5,  5,  and  9  pounds, 
respectively;  the  dotted  curve  shows  the 
speed  of  wheel  for  grinder  load. 

Mill  No.  50.—  This  is  a  12-foot 

Monitor  WOOden  power    mill    On    a     FIG.  45.—  .Diagram  showing  horsepower  of  mill 

36-foot  wooden  tower.     (See   flg. 

46.  )      It  is  a  Sectional  mill  and  has 
96   Sails,  each   44   by  4.25   by   1.75 

inches,  set  at  an  angle  of  34°  to  the  plane  of  the  wheel.  The  shaft 
is  geared  forward  3.66  to  1.  The  swivel  gearing,  which  enables  the 
mill  to  turn  easily  and  keep  full  in  the  wind,  is  shown  in  fig.  47. 
The  mill  is  used  for  shelling  and  grinding  corn  and  pumping  water. 
It  is  in  very  good  condition,  and  the  wind  exposure  is  very  good. 
The  mill  had  been  in  use  about  three  years.  The  mean  temperature 
during  the  time  of  test  was  83°  F.,  the  mean  barometric  pressure  28.6 
inches. 


loads  of  9,  5,  and  1.5  pounds,  respectively;  the 
Dotted  line  ^  shows  maximum  horsepower. 


MtTKPHY.] 


POWER    MILLS    TESTED. 


97 


FIG.  46.— Mill  No.  50— la-foot  wooden  Monitor 


P"TO.  47. — Swivel  gearing  of  mill  No.  50 — 1^-foot  wooden  Monitor. 


98  THE    WINDMILL. 

The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  50 — 12-foot  wooden  Monitor. 


[NO.  42. 


Load 
on 
brake. 

Load  per 
revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of  wind 
wheel  per  minute  at  given 
wind  velocities  (per  hour). 

Horsepower  of   mill  at    given  wind 
velocities  (per  hour). 

8  miles. 

12  miles. 

16  miles. 

30  miles. 

35  miles. 

8  miles. 

13  miles. 

s 

30  miles. 

I 
1 
8 

Lbs. 
0 
1.5 

& 

Ft.-lbs. 
0 
130 
314 

490 

16 

33 
35 

44 
35 

27 
10 

54 
43 
34 

34 

64 
53 
40 
30 

0.091 

0.137 
0.2510 
0.150 

0.  156 
0.334 
O.a57 

0.189 
0.381 
0.445 

The  revolutions  of  the  wind  wheel  for  three  brake  loads  (0,  1.5,  and 
2.875  pounds)  are  shown  in  fig.  48.     This  figure  also  shows  the  rmm- 


VELOCITY  OF   WIND   IN  MILES  PER  HOUR. 

10  15  30  35 

60 


VELOCITY  OP  WIND  IN   MILES  PER  HOUR. 

10  15  30  25 


45 


I- 


FIG.  48.— Diagram  showing  revolutions  of  wind 
wheel  of  mill  No.  50— 13-foot  wooden  Monitor. 
Curves  marked  0, 1.5, 3  £,  4.5  are  for  brake  loads 
of  0, 1.5, 2£,  and  4.5  pounds,  respectively. 


FIG.  49. — Diagram  showing  horsepower  of  mill 
No.  50— 12-foot  wooden  Monitor.  Curves 
marked  4.5,  2J,  and  1.5  are  for  brake  loads  of 
4.5,  2J,  and  1.5  pounds,  respectively;  dotted 
curve  DK  shows  maximum  power. 


ber  of  revolutions  for  a  4.5-pound 

load,  found  by  interpolation  from 

the  other  results.     This  mill  will 

be  seen  to  require  about  a  6- mile 

wind  to  start  it  without  any  load  and  to  make  only  64  revolutions 

per  minute  in  a  25-mile  wind.     The  12-foot  Aermotor  will  start  in  a 

4.5-mile  wind  and  make  87  revolutions  per  minute  in  a  25-mile  wind 

with  no  load.     Fig.  49  shows  the  horsepower  of  this  mill  for  the  four 

loads;  also  the  max i mum  horsepower. 

Mill  No.  62. — This  is  a  14-foot  Challenge  wooden  power  mill  on  a 
45-foot  wooden  tower,  manufactured  by  the  Challenge  Windmill 
Company,  of  I  Jalavia,  Illinois.  (See  fig.  50.)  It  is  a  sectional  mill,  and 
has  two  side  wheels  for  keeping  tho  main  wheel  in  the  wind.  The 


MURPHY.] 


POWER   MILLS    TESTED. 


99 


wind  wheel  has  102  sails,  each  51.5  by  5  by  1.75  inches,  set  at  an  angle 
of  39°  to  the  plane  of  the  wheel.  The  mill  works  a  sheller,  a  grinder, 
and  a  pump.  There  are  two 
horizontal  shafts,  one  of 
which  works  the  grinder  and 
sheller,  the  other  the  pump. 
The  shaft  that  works  the 
pump  is  12  feet  long  and  1.5 
inches  in  diameter;  it  is 
geared  forward  1. 5  to  1 .  The 
shaft  that  works  the  grinder 
is  6  feet  long  and  1.5  inches 
in  diameter ;  it  is  geared  for- 
ward 15.25  to  1.  The  well  is 
a  drilled  well,  192  feet  deep. 
The  lift  was  180  feet,  the  dis- 
charge 0.25  quart  per  stroke. 
The  water  is  pumped  into  a 
large  box,  and  passes  to 
watering  troughs  when 
needed.  The  pump  has  a 
counterweight  which  raises 
on  the  downstroke  and  assists 
in  lifting  the  water  on  the 
upstroke.  The  mean  tem- 
perature was  92°  F.,  the  mean  barometric  pressure  28.6  inches.  The 
results  of  the  tests  are  as  follows : 

Results  of  tests  of  mill  No.  52 — 14-foot  wooden  Challenge. 


FIG.  50.— Mill  No.  52— 14-foot  wooden  Challenge. 


Load 
on 
brake. 

Load  per 
revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of  wind 
wheel   per    minute    at    given 
wind  velocities  (per  hour). 

Horsepower  of  mill  at  given  wind 
velocities  (per  hour). 

CO 

12  miles. 

16  miles. 

20  miles. 

1 

81 

8  miles. 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

Lbs. 
0  
Pump 

2."""." 

Ft.-lbs. 
0 

7 

18 
14 

25 

22 
17 
8 

30 
27 
22 
16 

0.059 

0.093 
0.222 
0.210 

0.115 

0.287 
0.420 

432 

864 

The  revolutions  of  wind  wheel  per  minute  for  loads  of  0,  1,  and 
2  pounds  are  shown  in  fig.  51.  For  0  load  the  pump  shaft  was  run- 
ning with  the  pump  detached;  the  grinder  shaft  was  not  working. 
When  pumping  the  grinder  was  not  working.  When  the  brake  loads 
of  1  and  2  pounds  were  being  used  the  pump  shaft  was  not  work- 
ing. A  curve  was  obtained  giving  the  speed  of  the  wind  wheel  for 
no  brake  load  with  the  grinder  shaft  working  and  with  the  pump 
shaft  not  working.  This  curve  nearly  coincided  with  that  for  the 


100 


THE    WINDMILL. 


[NO.  42. 


pump  load,  showing  that  the  friction  of  the  grinder  shaft  was  about 
equal  to  the  pump  load.  With  the  pump  shaft  working,  but  not 
the  pump,  the  mill  will  be  seen  to  require  a  7-mile  wind  to  start  it, 
and  it  mak3S  only  30  revolutions  in  a  20-mile  wind.  Fig.  52  shows 
the  horsepower  of  this  mill. 

This  is  a  hard-running  mill;  there  is  too  much  friction.     The  side 
wheels  do  not  respond  to  changes  in  the  direction  of  the  wind  as  quickly 


VELOCITY  OF  WIND   IN  MILES  PER 
HOUR. 

10  15  2 


VELOCITY   OF   WIND    IN 
10  1' 


111 


Fie.  IA. — Diagram  showing  revolu- 
tions of  wind  wheel  of  mill  No.  52— 
14-foot  wooden  Challenge.  Curve 
marked  0  is  for  no  brake  load ;  curve 
P  is  for  pump  load;  curves  1  and  2 
are  for  brake  loads  of  1  and  2 
pounds,  respectively. 


FIG.  52. — Diagram  showiug  horsepower  of  mill  No. 
52— 14-foot  wooden  Challenge.  Curves  marked 
1  and  2  are  for  brake  loads  of  1  and  2  pounds, 
respectively;  curve  Pis  for  pump  load;  dotted 
curve  DK  shows  maximum  power. 


as  does  the  vane  or  rudder 
in  other  mills.  The  wind 
exposure  was  very  good  and 
the  mill  was  nearly  new. 

Mill  No.  53. — This  is  a  12-foot  Ideal  power  mill  on  a  33-foot  wooden 
tower.  The  wind  wheel  has  21  curved  sails,  each  43.25  by  16.5  by 
8.25  inches,  set  at  an  angle  of  32°  to  the  plane  of  the  wheel.  The 
horizontal  shaft  is  geared  forward  6.07  to  1.  The  mill  had  been  in 
use  about  four  years  for  shelling  and  grinding  corn.  Three  brake 
loads  were  used  in  the  test — 0,  1.5,  and  2.5  pounds.  The  mean  tem- 
perature during  the  tests  was  92°  F.,  the  mean  barometric  pressure 
28.7  inches.  The  results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  53 — 12-foot  Ideal. 


Load  on 
brake. 

Load  per 
revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of  wind 
wheel  per  inimite  at  given 
wind  velocities  (per  hour). 

Horsepower  of  mill  at  given  wind  ve- 
locities (per  hour). 

8  miles. 

12  miles. 

1 
1 

CO 

1 

2 
8 

25  miles. 

1 

1 

00 

12  miles. 

1 

a 

CD 

20  miles. 

OB 

_CD 

1 

£ 

Pounds. 
0 
1.5 
2.5 

Ft.-lbs. 
0 

272 
455 

25 

40 

29 

51 
41 
88 

60 

51 
44 

66 

til) 
54 

0.239 

o.  ;KW 

0.  440 

0.420 
0.60ti 

0.500 
0.745 

MURPHY.] 


POWEE   MILLS    TESTED. 


101 


Fig.  53  shows  the  number  of  revolutions  per  minute  of  the  wind 
wheel  for  the  three  brake  loads.  The  mill  will  be  seen  to  start  in 
about  a  5-inile  wind  and  to  make  6§  revolutions  a  minute  in  a  25-mile 
wind  with  no  load.  Fig.  54  shows  the  horsepower  for  the  several  loads. 

Mill  No.  5Jf. — This  is  a  12-foot  Aermotor  like  No.  27,  on  a  47-foot 
tower.  The  12-foot  Aermotor  No.  27  was  found  to  be  so  much  greater 
in  power  and  speed  than  other  12-foot  mills  tested  that  we  thought 


VELOCITY  OF  WIND  IN  MILES  PER  HOUK. 

10  15  2()  25 


§45 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

10  15  20  2) 

1.0 


FIG.  53. — Diagram  showing  revolutionsof  wind 
wheel  of  mill  No.  53— 12-foot  Ideal.  Curves 
marked  0, 1.5, 2.5,  and  3.5  are  for  brake  loads  of 
0, 1.5,  2.5,  and  3.5  pounds,  respectively. 


FIG.  54. — Diagram  showing  horsepower  of  mill 
No.  53— 12-foot  Ideal.  Curves  marked  3.5,  2.5, 
and  1.5  are  for  brake  loads  of  3.5,  2.5,  and  1.5 
pounds,  respectively;  dotted  curve  DK shows 
maximum  power. 


it  wise  to  test  another  of  the  same 
make  and  size  under  somewhat  different  conditions.  No.  54  had  been 
in  use  about  two  years.  Two  brake  loads  were  used — 0  and  297  foot- 
pounds per  revolution  of  wind  wheel.  The  mean  temperature  during 
the  test  was  92°  F.,  the  mean  barometric  pressure  29.2  inches.  The 
results  of  the  tests  are  as  follows: 

Results  of  tests  of  mill  No.  54 — 12-foot  Aermotor. 


Load  on 
brake. 

Load  per 
revolu- 
tion of 
wind 
wheel. 

Number  of  revolutions  of  wind 
wheel    per    minute   at   given 
wind  velocities  (  per  hour)  . 

Horsepower  at  given  wind  velocities 
(per  hour). 

8  miles. 

12  miles. 

1 

1 

?o 

I 

i 

8 

25  miles. 

8  miles. 

12  miles. 

| 

1 

<o 

1 

a 

3 

1 
1 

8 

Pounds. 
0 
1.75 

Ft.-lbs. 
0 
297 

31 

49 
38 

63 
52 

75 
63 

87 
75 

0.34 

0.46 

0.57 

0.68 

It  will  be  seen  that  the  results  of  the  tests  of  this  mill  apparently 
agree  closely  with  those  of  No.  27,  page  86.     The  agreement,  however, 


102 


THE    WINDMILL. 


[NO.  42. 


is  not  so  close  as  it  appears,  since  the  temperature  for  No.  54  is  much 
higher.  It  is,  however,  about  the  same  as  the  temperature  for  other 
mills,  so  that  we  can  still  use  the  results  found  for  mill  No.  27  in  com- 
paring its  power  and  speed  with  those  of  other  mills. . 

COMPARISON   OF  POWER  MILLS. 

Comparison  of  12-foot  Ideal  (No.  53)  with  14-foot  Ideal  (No.  34).— It 
must  be  remembered  that  in  this  and  in  all  other  comparisons  no  cor- 
rection is  made  for  difference  in  temperature  and  barometric  pressure. 
The  speeds  for  no  load  and  the  maximum  horsepowers  for  these  mills 
are  as  follows: 

Comparison  of  results  for  12-foot  Ideal  and  14-foot  Ideal. 


Mill. 

Number  of  revolutions  of 
wind  wheel  per  minute  at 
given  wind  velocities 
(per  hour). 

Maximum   horsepower    at 
given  wind  velocities 
(per  hour). 

8  miles. 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

1 

co 

12  miles. 

1 

a 

ce 

20  miles. 

25  miles. 

12-foot  Ideal 

25 

20 

1.07 

40 
34 

1  00 

51 

44 

0  99 

60 
53 

0  97 

68 
58 

1  00 

0.06 
0.06 

0.23 
0.22 

0.44 
0.46 

0.70 
0.74 

14-foot  Ideal 

Ratio  of  circumference 
velocities  (^f  ) 

It  will  be  seen  that  the  useful  power  of  the  14-foot  mill  is  very  little 
more  than  that  of  the  12-foot  mill,  and  that  the  circumference  veloci- 
ties are  nearly  the  same  for  no  load,  where  no  horizontal  shaft  is  being 
turned.  In  the  case  of  the  12-foot  mill  the  brake  was  on  the  foot 
gear  and  there  was  no  horizontal  shaft  to  turn,  but  in  the  case  of  the 
14- foot  mill  the  brake  pulley  was  on  a  shaft  15  or  20  feet  long.  We 
believe  that  if  the  brake  pulley  had  been  on  the  foot  gear  and  the 
line  shaft  thrown  out  of  gear,  so  as  to  eliminate  shaft  friction,  the 
mill  would  have  shown  at  least  10  per  cent  more  power.  The  tower 
obstructs  the  wheel  somewhat  and  reduces  the  power. 

Comparison  of  12-foot  Aermotor  (No.  27)  with  14-foot  Ideal  (No. 
84). — The  speeds  for  no  load  and  the  maximum  horsepowers  for  these 
mills  are  as  follows: 

Comparison  of  results  for  12-foot  Aermotor  and  14-foot  Ideal. 


Mill. 

Number  of  revolutions  of 
wind  wheel  per  minute  at 
given    wind  velocities 
(per  hour). 

Maximum    horsepower    at 
given   wind   velocities 
(per  hour). 

8  miles. 

12  miles. 

1 
jg 

1 

a 
a 

iO 

53 
1.21 

W 

£ 

1 

s 

87 

58 

1.28 

8  miles. 

12  miles. 

1 
1 

JS 

20  miles. 

12-  foot  Aermotor  

30 
80 

1.29 

49 
34 

1.23 

63 
44 

1.22 

0.09 
0.06 

0.38 

0.22 

0.66 
0.46 

1.05 
0.74 

14-foot  Ideal          

Ratio  of  circumference 
velocities  (12) 

MURPHY.] 


COMPARISON    OF    POWER    MILLS. 


103 


It  will  be  seen  that  the  number  of  revolutions  per  minute  of  the 
12-foot  mill  is  50  per  cent  greater  than  for  the  14-foot  mill.  This  is 
true  for  the  lower  as  well  as  for  the  higher  velocities,  where  the  gov- 
erning of  the  mill  does  not  enter  to  reduce  the  speed.  It  will  be  seen 
also  that  the  12-foot  mill  is  producing  from  42  to  50  per  cent  more 
horsepower  than  the  14-foot  mill.  The  temperature  was  49°  higher 
and  the  pressure  0.6  inch  lower  when  the  14-foot  mill  was  tested 
than  when  the  12-foot  mill  was  tested.  The  effect  is  to  lessen  the 
difference  between  the  power  and  speeds  of  the  mills. 

Comparison  of  12-foot  Aermotor  (No.  27)  with  16-foot  Aermotor 
(No.  44). — Attention  has  already  been  drawn  to  the  similarity  between 
the  speed  curves  of  these  mills  (figs.  35  and  42)  and  between  the  power 
curves.  (The  power  curves  for  mill  No,  44  are  shown  in  fig.  43;  those 
for  mill  No.  27  were  platted,  but  are  not  published  because  of  lack  of 
space. )  If  we  compare  the  number  of  revolutions  per  minute  for  no 
load,  we  shall  see  that  they  are  to  each  other  nearly  inversely  as  the 
diameter,  or  that  the  circumference  velocities  of  the  two  mills  are  the 
same  in  all  wind  velocities.  We  may  compare  the  brake  horsepower 
and  the  speed  as  follows: 

Comparison  of  results  for  13-foot  Aermotor  and  16-foot  Aermotor. 


Mill. 

Number    of    revolutions    of    wind 
wheel  per  minute  at  given  wind 
velocities  (per  hour). 

Maximum    horse- 
power    at   given 
wind  velocities 
(per  hour). 

8  miles. 

I 

1 

<M 

16  miles. 

20  miles. 

25  miles. 

10  miles. 

15  miles. 

1 
1 

8 

12-foot  Aermotor 

30 
23 

1.02 

49 

38 

1.03 

63 

48 

1.02 

75 
56 

0.99 

87.0 
64.5 

0.99 

0.21 

0.29 

1.38 

0.58 
0.82 

1.41 

1.05 
1.55 

1.48 

16-foot  Aermotor 

Ratio    of    circumfer- 
ence velocities  (yf  )  -  - 

From  this  it  will  be  seen  that  the  power  of  the  16-foot  Aermotor  is 
about  1.22  times  that  of  the  12-foot.  The  ratio  of  the  squares  of  the 
diameters  is  1.78;  the  ratio  of  the  diameters  1.33.  It  will  be  seen  that 
the  power  does  not  increase  as  the  squares  of  the  diameters,  as  is  often 
stated ;  it  increases  faster  than  as  the  diameters,  but  more  nearly  as 
the  diameters  than  as  the  squares  of  the  diameters. 

Comparison  of  16-foot  Althouse  wooden  mill  (No.  28)  with  16-foot 
Aermotor  (No.  44). — From  the  following  table  it  will  be  seen  that  the 
wind  wheel  of  No.  44  is  revolving  from  56  to  77  per  cent  faster  than 
the  wind  wheel  of  No.  28.  The  latter,  however,  has  to  overcome  the 
friction  of  10  or  12  feet  of  line  shafting.  It  will  be  seen  that  No.  44 
is  yielding  from  70  to  167  per  cent  more  power  than  No.  28.  The 
superiority  of  the  steel  mill  over  the  wooden  mill  is  very  evident  in 
this  case. 


104  THE    WINDMILL.  [NO.  42. 

Comparison  of  results  for  16-foot  Althouse  and  16-foot  Aermotor. 


Mill. 

Number  of  revolutions  of 
wind  wheel  per   minute 
at  given  wind  velocities 
(per  hour). 

Maximum    horsepower    at 
given    wind    velocities 
(per  hour). 

8  miles. 

12  miles. 

t 

1 

s 

20  miles. 

25  miles. 

8  miles. 

1 

16  miles. 

20  miles. 

16-  foot  Althouse. 

13 
23 

1  77 

23 

38 

1.65 

30 

48 

1.60 

36 
56 

1.55 

40.0 
64.5 

1.61 

0.06 
0.16 

2.67 

0.29 
0.48 

1.65 

0.52 
0.93 

1.78 

16-  foot  Aermotor 

1.55 

Ratio  of  circumference 
velocities  (steel) 

Vwood/  "  " 

Comparison  of  22. 5 -foot  Halliday  wooden  mill  (No.  49)  with  16-foot 
Aermotor  (No.  44)- — From  the  following  table  it  will  be  seen  that  the 
steel  mill  makes  about  two  revolutions  to  one  revolution  of  the  wooden 
mill,  and  that  its  power  is  from  41  to  167  per  cent  greater. 

Comparison  of  results  for  22.5-foot  Halliday  and  16-foot  Aermotor. 


Mill. 

Number  of   revolutions  of 
wind   wheel   per    minute 
at  given  wind  velocities 
(per  hour). 

Maximum    horsepower    at 
given    wind    velocities 
(per  hour). 

8  miles. 

12  miles. 

16  miles. 

1 

a 

8 

8  miles. 

12  miles. 

16  miles. 

20  miles. 

22.5-foot  Halliday 

11 
23 

1.48 

24) 

38 

i.a<> 

25 

48 

1.88 

30 
56 

1.32 

0.06 
0.16 

2.67 

0.34 
0.48 

1.41 

0.62 
0.93 

1.50 

0.88 
1.55 

1.76 

16-  foot  Aermotor  

Ratio  of  circumference 
velocities  (  !6Y  .. 

Comparison  of  12-foot  Aermotor  (No.  27)  with  22.5-foot  Halliday 
wooden  mitt  (No.  4^). — Comparing  the  power  of  these  mills,  Ave  have 
the  following: 

Comparison  of  results  for  13-foot  Aermotor  and  22.5-foot  Halliday. 


Mill. 

Number  of  revolutions  of 
wind   wheel    per   minute 
at   given   wind  velocities 
(per  hour). 

Maximum    horsepower    at 
given    wind    velocities 
(per  hour). 

8  miles. 

12  miles. 

16  miles. 

20  miles. 

8  miles. 

12  miles. 

16  miles. 

20  miles. 

12-  foot  Aermotor  ... 

30 
11 

1.46 

49 
20 

1.31 

n 

25 
1.34 

75 

30 

1.32 

0.09 
0.06 

1.50 

0.33 
0.32 

1.1)3 

0.66 
0.63 

1.05 

1.05 
0.  !»4 

1.12 

22  5-foot  Halliday 

Ratio  of  circumference 
velocities  Q~)  

It  will  be  seen  that  this  22.5-foot  wooden  mill  does  not  furnish  as 
much  power  as  a  good  12-foot  steel  mill. 


MURPHY.] 


COMPARISON    OF    POWER   MILLS. 


105 


Comparison  of  wooden  power  mills. — Of  the  mills  in  the  following 
table  the  12-foot  has  the  least  friction;  the  tower  being  in  front  of  the 
windmill  obstructs  the  wheel  and'  reduces  the  power.  The  14-foot 
mill  probably  has  more  friction  than  the  others.  The  16-foot  Irri- 
gator  has  too  few  sails ;  with  more  sails  the  power  could  probably  be 
increased  75  per  cent  or  more. 

Comparison  of  results  of  tests  of  wooden  power  mills. 


Number  of  revolutions  of 

wind  wheel  per  minute     Horsepower  at  given  wind 
at  given  wind  velocities            velocities  (per  hour). 

(per  hour). 

Mill 

CO 

V. 

t 

t 

1 

. 

$ 

t 

g 

J 

g 

1 

1 

1 

1 

1 

1 

1 

1 

CO 

a 

s 

8 

£ 

oo 

M 

s 

s 

12-foot  Monitor  (No.  50)  

16 
7 
13 
12 

33 
18 
23 
25 

44 
25 
30 
32 

54 
30 
36 
41 

64 

0.02 
0.01 
0.06 
0.02 

0.10 
0.10 
0.29 
0.16 

0.23 
0.25 
0.52 
0.30 

0.38 
0.42 
0.84 
0.44 

14-foot  Challenge  (No.  52).... 
16-foot  Althouse  (No.  28)  
16-foot  Irrigator  (No.  30)  

40 
44 

22.5-  foot  Halliday  (No.  49)  ... 

11 

20 

25 

30 



0.06 

0.32 

0.63 

0.94 

VELOCITY  OP  WIND    IN   MTLKS  PER   HOUR. 

5  10  15  2') 


35 


It  will  be  seen  that  the  16-foot  mill  (No.  28)  is  furnishing  from -2. 2 
to  2.9  times  more  useful  power  than  the  12-foot  mill  (No.  50).  It  will 
also  be  seen  that  the 
power  of  this  16-foot  mill 
compared  with  that  of  90 
the  12-foot  mill  increases 
faster  than  as  the  squares 
of  the  diameters,  while  75 
the  power  of  the  22. 5-foot 
mill  compared  with  that  » 
of  the  12-foot  mill  does  |  6<> 
not  increase  as  fast  as  the  Q 
squares  of  the  diameters,  £ 
and  the  power  of  the  22. 5-  §  45 
foot  mill  compared  with  g 
that  of  the  16-foot  mill  g 
does  not  increase  as  fast  g  30 
as  the  first  power  of  the  H 
diameters. 

Comparison  of  12-foot  15 
Monitor  wooden  mill 
(No.  50}  with  1%-footAer- 
moto-r  (No.  27)  and  with 
12-foot  Ideal  (No.  53).- 
Fig.  55  shows  the  speed, 
in  revolutions,  of  the 

wind  wheels  of  these  mills  for  no  useful  load.    The  friction  is  small  in 
each  case.     The  Monitor  has  a  swivel  gearing,  and  the  Ideal  has  a  ball 
IKR  42—01 3 


FIG.  55.— Comparative  diagram  of  revolutions  of  wind 
wheels  of  mills  Nos.  50,  53,  and  27.  Curve  aa'  is  for  12-foot 
Aermotor;  bb'  is  for  12-foot  Ideal;  <r' is  for  12-foot  Monitor. 


106 


THE    WINDMILL. 


[NO.  42. 


gearing  to  carry  the  weight  of  the  shaft,  both  of  which  reduce  the 
friction.  It  is  fair  to  say  that  the  friction  load  of  the  Aermotor  is  at 
least  as  great  as  that  of  the  other  mills.  It  will  be  seen  that  the  speed 
of  the  Ideal  is  noticeably  greater  than  that  of  the  Monitor;  and  that 
the  speed  of  the  Aermotor  is  much  greater  than  that  of  the  Ideal, 
especially  for  high  wind  velocities.  This  is  the  reason  the  Aermotor 
is  so  much  more  powerful  than  other  mills.  It  revolves  much  faster, 
and  the  power  is  directly  proportional  to  the  speed.  But  why  is  its 
speed  greater  for  the  same  load? 

Comparison  of  results  for  12-foot  Monitor,  12-foot  Ideal,  and  12-foot  Aermotor. 


Mill. 

Load 
per  rev- 
olution 
of  wind 
wheel. 

Number  of  revolutions  of 
wind  wheel   per  minute 
at  given  wind  velocities 
(per  hour). 

Horsepower  at  given  wind  veloc- 
ities (per  hour). 

8  miles. 

12  miles. 

16  miles. 

8 

25  miles. 

8  miles. 

CO 

9 
1 

a 

16  miles. 

8 

25  miles. 

12-foot  Monitor 
12-foot  Ideal  .  .  - 

12-foot  Aermo 
tor 

Ft.-lbs. 

f            ° 

\          120 

I         314 
0 

\         272 
I         455 
0 
222 
444 
[         666 

16 

88 

25 

44 
35 
27 
51 
41 
32 
63 
57 
48 
12 

54 
43 
34 
60 
51 
44 
75 
70 
65 
50 

64 
52 
40 

68 
60 
54 

87 
81 

77 
72 

0.091 

0.127 
0.230 

0.  156 
0.324 

0.189 
0.381 

25 

.  40 
49 

0.239 

0.338 
0.440 

0.420 
0.606 

0.500 
0.745 

30 
16 

29 
43 
23 

0.089 

0.285 
0.303 

0.386 
0.  653 
0.234 

0.458 
0.890 
1.028 

0.523 
1.020 
1.451 

The  dimensions  of  the  principal  parts  of  the  wind  wheels  of  these 
mills  and  the  mean  temperature  and  pressure  when  the  tests  were 
made  are  as  follows: 

Dimensions  of  principal  parts  of  mills  Nos.  50,  53,  and  27. 


Mill. 

Num- 
ber 
of 

Dimensions 
of  sails. 

Angle 
of 

sails. 

Inches. 

o 

12-foot  Monitor  (No.  50)  
12-foot  Ideal  (  No.  53  )  

96 
21 

44  x  4±xlf 

34 
32 

12-foot  Aermotor  (No.  27)... 

18 

44  xlSfxTj 

31 

Mean 

Mean 

baro- 

Gearing. 

temper 

metric 

ature. 

pres- 

sure. 

0^ 

Inches. 

3.66:1 

'83 

28.6 

6.  07  :  1 

92 

28.7 

6.00:1 

46 

28.9 

The  temperature  when  the  12-foot  Aermotor  was  tested  was  much 
lower  than  when  the  other  two  mills  were  tested,  but,  as  already 
stated,  the  temperature  when  Aermotor  No.  54  was  tested  was  92°  F., 
and  it  showed  a  speed  and  power  about  the  same  as  Aermotor  No.  27; 
so  we  may  leave  this  difference  in  temperature  out  of  account. 

It  will  be  seen  that  the  Monitor  is  not  geared  forward  as  much  as 
the  other  two,  but  this  docs  not  affect  the  speod  for  no  load.  The 
sail  angle  is  about  the  same  for  all,  also  the  length  of  sail;  but  the 


MURPHY.]        PUMPING    MILLS    AND    POWER    MILLS    COMPARED. 


107 


VELOCITY  OK  WIND   IN  MT17ES  PER   HOUR. 
5  10  15  20 


l.i 


l.o 


0.8 


o.t: 


t 


number  of  sails  and  the  width  are  quite  different.  The  Aermotor  has 
few  sails,  but  of  large  size ;  the  Ideal  has  more  and  somewhat  smaller 
sails ;  the  Monitor  has  many  small  sails,  and  its  tower  is  located  in 
front  of  the  wind  wheel.  Its  sails  are  plane,  instead  of  curved,  all  of 
which  tends  to  decrease  its  power. 

Fig.  56  shows  the  curves  of  maximum  horsepower.  It  will  be  seen 
that  the  difference  between  the  horsepower  of  the  Aermotor  and  that 
of  the  Ideal  is  about  the  same  as  the  difference  in  their  speeds  for  the 
same  wind  velocity,  but 
the  difference  between 
the  power  of  the  Mon- 
itor and  that  of  the  Ideal 
is  much  greater  than  the 
corresponding  difference 
in  their  speeds.  The 
wooden  mill,  therefore, 
not  only  has  a  less  speed 
at  a  given  wind  velocity 
than  the  steel  mill,  but 
it  carries  a  proportion- 
ately less  load.  For  ex- 
ample, in  a  20-mile  wind 
a  load  of  120  foot-pounds 
per  revolution  reduces 
the  speed  of  the  Monitor 
from  54  to  43  (or  11) 
revolutions  per  minute, 
while  in  the  case  of  the 
Aermotor  a  load  of  220 
foot-pounds  (about  80 
per  cent  greater)  reduces 
the  speed  from  75  to.  70 
(only  5)  revolutions  per  minute.  In  the  case  of  the  Ideal  a  load  of 
272  foot-pounds  per  revolution  (2.3  times  the  load  of  the  Monitor) 
reduces  the  speed  from  60  to  51  (or  9)  revolutions  per  minute. 

COMPARISON  OF  PUMPING  MILLS  WITH   POWER  MILLS. 

Comparison  of  12- foot  pumping  mill  (No.  3)  with  12 -foot  power  mill 
(No.  27}. — The  load  per  stroke  of  No.  3  (see  page  30,  Part  I)  is  415.3 
foot-pounds.  The  wind  wheel  makes  3.3  revolutions  to  1  stroke  of 
the  pump,  so  that  the  load  per  revolution  of  wind  wheel  is  124.5  foot- 
pounds. This  is  less  than  the  smallest  load  used  in  testing  No.  27,  viz, 
222  foot-pounds  per  revolution.  A  diagram  was  platted  showing  the 
useful  work,  in  horsepower,  of  these  mills  for  these  loads.  The  curve 
for  the  pumping  mill  was  seen  to  start  with  a  little  less  wind  velocity 
than  that  of  the  power  mill,  indicating  a  somewhat  less  total  load. 


FIG.  56.— Comparative  diagram  of  horsepower  of  mills  Nos. 
50, 53,  and  27.  Curve  aa'  is  for  12-foot  Aermotor;  bb'  is  for 
12-foot  Ideal;  cc'  is  for  12-foot  wooden  Monitor. 


108  THE    WINDMILL.  [NO. 42. 

Comparing  the  ordinates  of  these  curves  for  different  wind  velocities, 
the  following  ratios  were  obtained,  which  give,  approximately,  the 
pump  efficiency,  no  allowance  being  made  for  difference  in  temperature 
and  pressure: 

8  12  16  20  25  30 

0.60        0.53        0.54        0.54        0.58        0.58 

The  mean  of  these  ratios  is  0.56.  If  the  useful  load  of  the  pumping 
mill  had  been  somewhat  greater,  so  that  the  mills  would  have  started 
at  the  same  wind  velocity,  the  ratio,  or  pump  efficiency,  would  be 
about  60  per  cent,  which  is  about  what  might  be  expected  of  this  pump 
under  this  lift.  The  ratio  of  the  useful  loads  is  125-7-222=0.57.  This 
ratio  would  probably  be  about  0.60  if  the  loads  were  such  that  the 
mills  would  start  at  the  same  wind  velocity. 

Comparison  of  16-foot  pumping  Aermotor  (No.  9)  with  16-foot  power 
Aermotor  (No.  44). — The  useful  load  of  No.  0  (see  pages  36  to  37, 
Part  I)  is  1,013  foot-pounds  per  stroke  of  pump,  or  304  foot-pounds  per 
revolution  of  wind  wheel.  The  smallest  useful  load  of  No.  44  is  528 
foot-pounds  per  revolution  of  wind  wheel.  A  diagram  was  platted 
showing  the  useful  horsepower  of  these  mills  for  these  loads.  For  this 
particular  load  (1,013  foot-pounds)  the  pumping  mill  was  seen  to  start 
at  a  somewhat  less  wind  velocity  than  the  power  mill,  indicating  that  the 
total  load  of  the  pumping  mill  was  somewhat  less  than  that  of  the  power 
mill.  The  ratio  of  any  two  of  the  ordinates  gave,  approximately,  the 
pump  efficiency  for  that  wind  velocity,  the  difference  in  temperature 
and  pressure  being  neglected. 

These  ratios  for  four  velocities  are  as  follows : 

12  16  20  25 


0.72        0.67        0.69       0.63 

If  the  pump  load  had  been  somewhat  greater — such  that  the  mills 
would  start  at  the  same  wind  velocity — the  mean  ratio  would  be  about 
70  per  cent.  This,  again,  is  about  what  is  expected  for  the  efficiency  of 
this  pump,  which  is  somewhat  better  than  mill  No.  3  and  has  a  higher 
lift.  The  ratio  of  the  useful  loads  of  these  mills  is  304  -f-  528  =  0.57. 
This  ratio  would  probably  be  about  60  per  cent  if  the  mills  started  at 
the  same  wind  velocity. 


MURPHY.]        PUMPING    MILLS    AND    POWER   MILLS    COMPARED. 


109 


It  is  interesting  to  compare  the  performance  of  these  mills  still 
further.    The  speeds  of  the  wheels  and  the  horsepowers  are  as  follows : 

Comparison  of  results  for  16-foot  pumping  Aermotor  and  16-foot  power  Aermotor. 


Number  of  revolu- 

tions of  wind  wheel 
per  minute  at  given 
wind    velocities 

Horsepower   at   given 
wind  velocities  (per 
hour). 

Load 

(per  hour). 

per 
revolu- 

Mill. 

tion  of 

. 

03 

DO* 

00                     02 

03 

wind 

r2 

Js 

| 

A 

j 

£ 

,2 

| 

wheel. 

g 

a 

a 

a 

a 

a 

g 

a 

3 

s 

8 

8 

2 

5D 

§ 

8 

Ft.-lbs. 

16-foot  pumping  mill  (No.  9). 
16-foot  power  mill  (No.  44)... 

31 

28 

42 

41- 

52 

50 

59 

58 

0.325 
0.45 

0.433 
0.65 

0.548 
0.80 

0.601 
0.95 

0.304 
0.528 

Ratio  of  pump  power  to  mill 
power   ' 

0.72 

0.67 

0.69 

0.63 

0.58 

It  will  be  seen  that  the  wind  wheel  of  the  pumping  mill  is  making 
from  one  to  two  more  revolutions  per  minute  than  that  of  the  power 
mill. 

Comparison  of  22.5-foot  pumping  mill  (No.  36)  with  22. 5 -foot  power 
mill  (No.  49). — In  this  comparison  we  will  use  the  curve  of  5  pounds, 
or  1,087  foot-pounds,  per  revolution  of  wind  wheel  as  the  speed  for 
this  load,  corresponding  more  nearly  with  that  for  the  pump  load 
than  any  other.  The  speeds  of  the  mills  and  the  horsepowers  are  as 
follows : 

Comparison  of  results  for  22. 5- foot  pumping  mill  and  22. 5- foot  power  mill. 


Number  of  revolu- 

tions of  wind  wheel 
per  minute  at  given 
wind    velocities 

Horsepower   at    given 
wind  velocities  (per 
hour). 

Load 

(per  hour). 

per 
revolu- 

00 

4 

4 

. 

00 

4 

« 

wind 

J 

£ 

| 

£ 

J 

J 

i 

r2 

wheel. 

a 

i 

a 

a 

| 

a 

a 

a 

IN 

CO 

3 

8 

2 

2 

8 

8 

Ft.-lbs. 

22.5-foot  pumping  mill  (No.  36).. 
22.5-foot  power  mill  (No.  49)  
Ratio  of  pump  power  to  mill 

12 
11 

17 
18 

20 
22 

24 
26 

0.090 
0.342 

0.124 
0.593 

0.150 
0.724 

0.182 
0.856 

0.248 
1.087 

power 

0.26 

'0.20 

0.20 

0.22 

0.23 

The  efficiency  of  the  pump  is,  therefore,  not  more  than  22  per  cent. 
The  ratio  of  useful  loads  is  22  per  cent.  (For  description  of  pumping 
mill  No.  36,  see  pages  52  to  53,  Part  I.) 


110 


THE    WINDMILL. 


EFFECT  OF    TENSION   OF    SPRING  ON    SPEED  AND    HORSEPOWER 

OF  MILL. 

The  effect  of  tightening  the  spring  which  holds  the  wind  wheel  of 
mill  No.  18  in  the  wind  has  been  shown  on  page  44,  Part  I.  The  effect 
of  a  reduction  in  the  tension  of  the  spring  of  the  16-foot  power  mill 

(No.  44)  is  shown  in  fig.  57.  The 
curve  aa'  is  for  no  load  and  the 
spring  new  and  stiff.  The  curve 


VELOCITY  OF  WIND   IN   MILES  PER  HOUR. 
10  15  20 

75 


W 

P 
£    45 

E 

h 

O 


80 


15 


aa' 


is  for  the  same  load  (none) 
and  spring  after  the  mill  had 
been  out  of  use  about  eight 
months.  It  will  be  seen  that 
these  curves  coincide  up  to  a 
velocity  of  about  10  miles  an 
hour,  after  which  they  separate 
rapidly.  In  a  25-mile  wind  the 
number  of  revolutions  of  the 
wind  wheel  per  minute  has  been 
reduced  from  64.5  to  54  by  the 
decrease  in  the  tension  of  the 
spring.  The  curve  bb'  is  for  a 
3-pound  brake  load  with  relaxed 
spring.  It  will  be  seen  to  be 
nearly  parallel  to  the  curve  aa", 
showing  that  the  effect  of  the 
load  when  the  spring  is  relaxed 
is  similar  to  that  when  it  is  taut. 
We  see  how  important  a  factor 

tension  of  spring  is  on  the  power  of  a  mill.  It  also  shows  that  if  a 
spring  is  to  be  used  in  place  of  a  weight  there  should  be  some  easy 
way  to  change  its  tension. 

MATHEMATICAL  DISCUSSION  OF  TESTS  OF  TWO  AERMOTORS. 

In  this  discussion  the  wind  velocities  are  those  found  by  the  use  of 
the  Robinson  cup  anemometer.  A  comparison  of  these  velocities  with 
true  wind  velocities  will  be  given  later.  The  Aermotors  are  selected 
for  this  discussion  because  their  power  is  greater  than  that  of  any  other 
form  of  mill  that  we  have  tested,  and  because  their  speed  and  power 
curves  are  derived  from  a  greater  number  of  observations  than  those 
of  any  other  mill. 

Discussion  of  tests  of  12-foot  Aermotor  (No.  27). — The  curves  showing 
the  number  of  revolutions  of  wind  wheel  (called  speed  curves)  of  this 
mill  for  four  brake  loads  are  given  on  page  88 — fig.  35.  Each  of  these 
curves  is  seen  to  resemble  a  parabola  the  axis  of  which  is  the  x  coor- 
dinate axis  on  which  the  wind  velocities  are  marked.  Each  of  these 
has  the  form  y*  =  a  +  bx,  in  which  x  is  the  wind  velocity  in  miles  per 


PIG.  57.— Diagram  showing  effect  of  tension  of 
spring  of  mill  No.  44— 16-foot  Aermotor.  Curve 
aa'  is  for  no  load,  spring  new  and  stiff;  aa"  is 
for  no  load,  spring  relaxed,  mill  having  been  out 
of  use  eight  months;  bb'  is  for  3-pound  brake 
load  with  relaxed  spring. 


MURPHY.] 


MATHEMATICAL    DISCUSSION. 


Ill 


hour,  y  the  speed  of  wind  wheel  in  revolutions  per  minute,  and  a  and 
b  constants.  For  the  curve  of  no  load  (0)  we  have  y  =  50  when  x  =  1 2, 
and  y  =  75  when  x  =  20.  Hence  we  have 

502  =  a  4- 126,  and 
752  =  a  +  206. 

Solving  these,  for  a  and  6  we  have  a  =—  2,187  and  6  =  391;  and  the 
equation  of  the  curve  is 

if=  -2,187  + 391.x.  (1) 

For  the  speed  curve  of  2  pounds  we  see  that  y  =  43  when  x  =  12,  and 
that  y  =  70  when  .7;  =  20.  Hence  we  have 

432  =  a  +  126,  and 
702  =  a  +  206. 

Solving  these,  we  have  a  =—2,728  and  6  =  381;  and  we  have  the 
equation  of  this  2-pound  curve 


y2  =  -  2,728  +  381aj. 


(2) 


Proceeding  in  a  similar  way,  we  have  for  the  equation  of  the  4-pound 

curve 

y*=  -4,384  +  424^.  (3) 

For  the  equation  of  the  6-pound  curve  we  have 

if  =  -  9,400  +  595x.  (4) 

The  speed  as  determined  by  measurement  and  as  found  from  these 
oquations  for  several  wind  velocities  is  shown  the  following  table. 

The  starting  velocities  are  found  by  making  y  =  0  and  solving  for  x 
in  equations  1  to  4. 


Table  allowing  revolutions  per  minute  of  12-foot  Aermotpr  (No.  27)  under 
loads  and  at  different  wind  velocities. 


Wind  velocity  per  hour. 

No  load. 

2-pound  load. 

4-pound  load. 

6-pound  load. 

Meas- 
ured. 

Com- 
puted. 

Meas- 
ured. 

Com- 
puted. 

Meas- 
ured. 

Com- 
puted. 

Meas- 
ured. 

Com- 
puted. 

8  miles  

Rev. 
30 
49 

63 

75 
87 
4.5 

Rev. 
30 
50 
64 
75 
87 
5.6 

Rev. 
16 
43 

57 
70 
81 
7.0 

Rev. 
18 
43 
58 
70 
82 
7.1 

Rev. 

Rev. 

Rev. 

Rev. 

12  miles 

23 

48 
65 

77 
10.2 

27 
49 
64 
78 
10.3 

16  miles 

12 
50 
72 
15.3 

10 
50 

74 
15.8 

20  miles  

25  miles  ...  .  
Starting  velocity  -  . 

If  the  origin  of  coordinates  for  equation  1  be  moved  to  the  point 
where  the  curve  crosses  the  axis  of  x,  the  equation  will  then  be  of  the 


112  THE    WINDMILL.  [NO.  42. 


form  ?/2  =  391ie',  from  which  we  have  y  =--  \X391x';  that  is,  the  speed 
for  a  constant  load  increases  as  the  square  root  of  the  wind  velocity. 

The  close  agreement  between  the  measured  and  computed  speeds, 
especially  for  the  curve  of  no  load,  is  noticeable.  The  measured  and 
computed  starting  velocities  differ  somewhat.  This  was  expected, 
since  it  is  difficult  to  get  the  starting  velocities  from  observation. 

Hereafter  in  this  discussion  the  computed  instead  of  the  observed 
speeds  and  starting  velocities  will  be  used.  It  must  be  remembered, 
however,  that  these  are  not  what  may  be  called  theoretical  results. 
They  are  obtained  from  measurements,  not  from  theory,  and  are  the 
adjusted  values  of  the  observed  quantities. 

The  power  curves  for  this  mill  for  three  brake  loads  were  platted,  but 
are  not  published  because  of  lack  of  space.  The  curves  are  parab- 
olas with  their  axes  horizontal.  This  follows  at  once  from  the  fact 
that  the  corresponding  speed  curves  are  parabolas.  The  power  is 
proportional  to  the  product  of  the  load  and  speed.  When  the  load  is 
constant,  as  it  is  for  one  of  these  speed  curves,  the  power  varies  as  the 
speed,  and  hence  the  load  curves  are  parabolas. 

The  equation  of  any  one  of  the  curves — as,  for  example,  the  2-pound 
curve — may  be  found  as  follows:  The  formula  for  horsepower  is 
H.  P.  =  2  n  EuL  +  33,000,  E  =  35.5  +  12  and  L  =  2.  Hence  IT.  P.  = 
2  X  22+7  x  6  x  35.5  x  2  x  i^  12  x  33,000  =  0.0067^  =  Ku  where  K 
=  0.0067. 

In  the  speed  equations  u  is  what  we  have  called  y,  and  y  =  —  2,728 
+  .381a5.  Hence— 

H.  P.  =  Ky  =  K*l  —  2,728  +  3Slo5,  and 

(H.  P.)2  =  JT2(- 2,728+  38105)  =  —0.1225+  0.017o?.  (5) 

In  the  diagram  of  power  curves,  platted  but  not  reproduced  here, 
the  curve  of  maximum  power  was  found  to  resemble  a  parabola  the 
axis  of  which  was  vertical  with  its  vertex  on  the  y  coordinate  axis  below 
the  origin.  The  form  of  its  equation  is  x2  =  a  +  by,  x  being  the  wind 
velocity,  in  miles  per  hour,  y  the  horsepower,  and  a  and  b  constants. 
For  x  =  5,  y  =  0,  and  for  x  =  20,  y  =  1.05.  Substituting  these  values 
in  the  above  equation  we  have:  25  =  a,  and  400  =  a  +  1.056.  From 
these  we  have:  a  =  25,  6  =  357,  and  the  equation  of  the  maximum 

power  curve  is — 

x2  =  25  +  357y.  (6) 

For  x  =  5,  10,  15,  20,  and  25,  y  has  the  values  0,  0.21,  0.56,  1.05,  and 
1.69,  which  agree  closely  with  those  taken  from  the  curve. 

For  the  mill  to  yield  the  greatest  amount  of  power  possible  the  load 
should  increase  as  the  wind  velocity  increases.  In  an  8.5-mile  wind 
a  2-pound  load  gives  the  maximum  power;  in  a  14-mile  wind  a  4-pound 
load  gives  the  maximum  power,  and  in  a  21-mile  wind  a  6-pound  load 
gives  the  maximum  power. 

We  wish  to  determine  how  the  load  and  speed  of  the  mill  vary  with 


MURPHY.] 


MATHEMATICAL    DISCUSSION. 


113 


the  wind  velocity  for  the  curve  of  maximum  power.  The  load  curves 
were  found  to  be  tangent  to  the  curve  of  maximum  power  for  loads 
and  velocities  about  as  follows:  The  0  curve  is  tangent  at  #  =  5,  the 
2-pound  curve  at  x=  8.5,  the  4-pound  curve  at  x  =  21.  For  a  con- 
stant increment  of  2  pounds  in  the  load  the  increment  of  wind  velocity 
changed  from  3.5  miles  to  7  miles.  Hence  the  velocity  increases 
faster  than  the  loading.  For  each  of  these  four  points  on  the  curve 
the  load  and  horsepower  are  known.  Hence  we  can  find  the  number 
of  revolutions  from  the  equation— 

H.  P.  =  2  X  n  x  R  X  n  x  4  x  L  4-  33,000.  (7) 

The  wind  velocities,  loads,  powers,  and  speeds  for  these  four  points 
of  tangencjr  are  as  follows: 

Data  regarding  points  of  tangency  of  power  curves  with  curves  of  maximum  power 

of  Aermotor  No.  27. 


Wind  velocity  per  hour. 

Load. 

Horsepower. 

Revolutions 
per  minute. 

5  miles 

Pounds. 

0 

0 

0 

8.5  miles     

2 

0.13 

19 

14  rnilfis 

4 

0.50 

38 

21  miles 

6 

1.15 

57 

The  speeds,  in  revolutions,  as  here  given  are  platted  in  fig.  35,  giv- 
ing the  curve  P§,  which  is  the  speed  curve  for  maximum  power.  The 
proper  load  for  maximum  power  can  now  be  found  for  any  wind  veloc- 
ity from  equation  7,  the  speed  being  taken  from  this  speed  curve. 
The  ratio  of  the  speed  at  maximum  load  to  the  speed  at  0  load,  for 
the  wind  velocities  10,  15,  and  20  miles  an  hour,  is  0.63,  0.70,  and  0.74, 
respectively,  showing  quite  an  increase.  The  following  table  gives 
additional  information  in  regard  to  speed  and  load  for  the  curve  of 
maximum  power: 

Data  regarding  speed  and  load  for  curve  of  maximum  power  of  Aermotor  No.  27. 


Wind  velocity 
per  hour. 

Load  per 
revolution 
of  wind 
wheel. 

Revolu- 
tions per 
minute. 

L  —  L'. 

S-S'. 

LS. 

LS  — 

L'S'. 

A*. 

5  miles 

Pounds. 

0 

o 

10  miles  ... 

2.1 

25 

2.1 

25 

52.5 

52.5 

15  miles  
20  miles  

4.0 
5.9 

41 
55 

1.9 
1.9 

16 
14 

160.4 
324.5 

107.9 
164.1 

55.4 
56.2 

The  fourth  column  gives  the  differences  between  the  successive 
loads,  or  the  increments  of  loading.  These  are  seen  to  decrease  some- 
what, showing  that  the  load  does  not  increase  quite  as  fast  as  the 
wind  velocit}7.  The  fifth  column  gives  the  differences  between  the 
successive  speeds,  and  shows  that  the  speed  does  not  increase  quite 


114 


THE    WINDMILL. 


[NO.  I-J. 


as  fast  as  the  wind  velocity.  The  sixth  column  gives  the  products  of 
the  loads  and  speeds,  which  is  proportional  to  the  horsepower.  The 
seventh  column  gives  the  increments  of  horsepower,  the  eighth  col- 
umn the  difference  between  the  figures  in  the  seventh  column.  These, 
being  nearly  constant,  show  that  the  curve  of  maximum  power  is  of 
the  second  degree. 

The  following  table  contains  additional  interesting  information  in 
regard  to  the  speed  of  this  mill : 

Data  in  regard  to  speed  of  mill  No.  27 — 12-foot  Aermotor. 


Wind  velocity  per 
hour. 

Revolu- 
tions per 
minute, 
no  load. 

Circumfer- 
ence velocity, 
in  miles, 
no  load. 

Ratio  of  cir- 
cumference 
velocity  to 
wind  velocity, 
no  load. 

Revolu- 
tions per 
minute  at 
maximum 
load. 

Ratio  of 
speed  at 
maximum 
load  to  speed 
at  no  load. 

8  miles 

30 

12.9 

1.61 

17 

0.57 

12  miles 

49 

21.0 

1.75 

32 

0.65 

16  miles     .  .. 

63 

27.0 

1.70 

44 

0.70 

20  miles  

75 

32.1 

1.60 

54 

0.72 

25  miles 

87 

37.3 

1.50 

The  results  obtained  from  this  12-foot  mill  may  be  stated  as  follows, 
in  terms  of  cup  anemometer  velocities: 

(1)  The  speed  of  the  wheel  for  a  constant  load  varies  as  the  square 
root  of  the  wind  velocit}^. 

(2)  The  speed  of  the  wheel  for  maximum  load  increases  slightly 
faster  than  the  first  power  of  the  wind  velocity. 

(3)  The  power  of  the  mill  for  a  constant  load  varies  as  the  square 
root  of  the  wind  velocity. 

(4)  The  maximum  power  of  the  mill  varies  as  the  square  of  the 
wind  velocity. 

(5)  The  load  for  maximum  power  does  not  increase  quite  as  fast  as 
the  wind  velocity. 

(6)  The  ratio  of  speed  for  maximum  load  to  the  speed  for  no  load 
increases  somewhat  with  the  wind  velocity. 

Discussion  of  tests  of  16-foot  Aermotor  No.  44-  —  The  speed  curves 
for  this  mill  are  shown  in  fig.  42.  They  are  seen  to  resemble  the 
parabolas  with  horizontal  axis.  The  equation  of  each  has  the  form 
y*=a-}-bx,  y  being  the  speed  in  revolutions  per  minute,  x  the  wind 
velocity  in  miles  per  hour,  and  a  and  b  being  constants  for  any  curve. 
We  see  that  for  #=12,  t/=38,  and  that  for  ^=20,  y=56.  Hence  we 

have 

382=a+  12fo,  and 
562=tt+20&. 


Solving  these  equations,  we  have  a—  — 1,094, 
tion  of  the  no-load  speed  curve  is 

y=  — 1,004+211. 5x. 


=  211.5,  and  the  equa- 


(8) 


MURPHY.] 


MATHEMATICAL  DISCUSSION. 


115 


Proceeding  in  a  similar  way,  we  have  for  the  equation  of  the  3-pound 
load  speed  curve 

2/2=-l,790+214.5#.  (9) 

For  the  5-pound  load  we  have 

2/2=-2,304+212#.  (10) 

For  the  8-pound  load  we  have 

y2=— 2,715+197#.  (11) 

The  speed  and  starting  velocities  as  computed  from  these  equations 
and  as  found  by  measurement  are  as  follows : 

Speed  and  starting  velocities  for  16-foot  Aermotor  No.  44. 


Wind  velocity  per  hour. 

No  load. 

3-pound  load. 

5-pound  load. 

8-pound  load. 

Meas- 
ured. 

Com- 
puted. 

Meas- 
ured. 

Com- 
puted. 

Meas- 
ured. 

Com- 
puted. 

Meas- 
ured. 

Com- 
puted. 

8  miles 

23.0 

38.0 
48.0 
56.0 
64.5 
4.5 

24.0 

38.0 
48.0 
56.0 
65.0 
5.1 

12  miles 

28.0 
41.0 
50.0 
59.0 

8.0 

28.0 
40.0 
50.0 
60.0 
8.3 

13 
33 
44 
54 
11 

15.0 
33.0 
44.0 
54.0 
10.9 

"i6."6" 

36.0 
47.0 
14.5 

"20.6" 
35.0 
47.0 
13.8 

16  miles 

20  miles            .     . 

25  miles 

Starting  velocity  .. 

The  computed  values  are  seen  to  agree  closely  with  the  measured 
values,  so  that  these  speed  curves  are  parabolas  of  the  form  y=  </a+bx. 
The  power  curves  shown  in  fig.  43  are  parabolas  of  this  form  for  the 
reason  given  for  the  corresponding  case  of  the  12-foot  Aermotor.  The 
curve  of  maximum  power  to  which  these  power  curves  are  tangent  is 
a  parabola  with  its  axis  vertical.  Its  equation  has  the  form  x2=a  +  ~by. 
We  may  obtain  the  data  for  finding  the  value  of  a  and  6  by  observing 
that  when  #=10,  ?/=0.30;  and  that  when  #=20,  y=l.55. 

We  have 

102=a+0.30Z>,  and 
202=u+1.556. 

Solving  these,  we  have  a =28,  6=240,  and  the  equation  of  the  curve  is 
#2=28+240?/.  (12) 

The  values  of  y  for  four  values  of  x  are  #=8,  t/=l5;  #=12,  ?/=0.48; 
#=16,  |/  =  0.f)5;  and  #=20,  y=l.55.  It  will  be  seen  that  these  values 
agree  closely  with  the  measured  horsepower  for  these  velocities.  By 
making  #=0  in  equation  12  we  have  y—  —0.125.  The  vertex  of  this 
maximum  power  curve  is  at  a  distance  0.125  below  the  axis  of  x.  If 
the  origin  of  coordinates  be  changed  to  this  point,  equation  12  will 


116 


THE    WINDMILL. 


[NO.  42. 


take  the  form  x2=Ky',  K  being  a  constant  and  y'  the  horsepower 
referred  to  the  new  origin.  Hence  we  see  that  the  maximum  horse- 
power varies  as  the  square  of  the  wind  velocity. 

To  find  the  variation  of  the  speed  and  load  for  this  curve  DK,  we 
notice  that  the  3-pound  curve  is  tangent  at  #=10.5,  the  5-pound  curve 
at  #=14,  the  8-pound  curve  at  #=19,  and  the  11-pound  curve  at  #=24. 
The  horsepower  is  known  at  these  points,  so  that  the  speed  can  be 
found  from  equation  7. 

The  wind  velocity,  load,  horsepower,  and  speed  for  each  of  these 
points  are  as  follows : 

Data  regarding  points  of  tangency  of  power  curves  with  c,urves  of  maximum  power 

of  Aermotor  No.  27. 


Wind  velocity  per  hour. 

Load. 

Horsepower. 

Revolutions 
per  minute. 

5  miles          ..     

Pounds. 
0 

0 

0 

10  5  miles 

3 

0.33 

21 

14  miles 

5 

0.70 

26 

19  miles 

8 

1.40 

33 

24  miles 

11 

2.17 

37 

The  speeds  here  found  are  platted  in  fig.  42,  giving  the  curve  PQ, 
which  gives  the  speed  of  the  wheel  for  the  maximum  load.  This  curve 
is  seen  to  be  a  nearly  straight  line  for  velocities  above  9  or  10  miles 
an  hour.  Hence  we  may  say  that  the  speed  increases  as  the  first 
power  of  the  wind  velocity  for  maximum  power. 

The  load  for  any  wind  velocity  can  now  be  found  from  the  formula 
176  Lu 


H.  P.  = 


,  the  speed  being  taken  from  the  speed  curve  PQ. 


33,000 

Or  the  loads  can  be  measured  from  the  load  curve  RS,  fig.  42.  This 
load  curve  (RS)  for  maximum  power  is  seen  to  be  a  straight  line,  show- 
ing that  for  wind  velocities  above  9  or  10  miles  an  hour  the  load  for 
maximum  power  varies  nearly  as  the  first  power  of  the  wind  velocity. 
The  following  table  contains  some  interesting  facts  in  regard  to  the 
working  of  this  mill : 

Data  in  regard  to  speed  of  mill  No.  44 — 16-foot  Aermotor. 


No  load. 

Maximum  load. 

Ratio  of 

speed  at 

Wind  velocity 
per  hour. 

Revolu- 
tions per 
minute. 

Circum- 
ference 
velocity 
in  miles. 

Ratio  of 
circum- 
ference 
velocity 
to  wind 

Revolu- 
tions per 
minute. 

Circum- 
ference 
velocity 
in  miles. 

Ratio  of 
circum 
ference 
velocity 
to  wind 

maxi- 
mum 
load  to 
speed  at 
no  load. 

velocity. 

velocity. 

Smiles 

23 

13.2 

1.67 

15 

8.6 

1.08 

0.65 

12  miles  

38 

21.7 

1.81 

23 

13.2 

1.10 

0.61 

16  miles  

48 

27.4 

1.71 

29 

16.6 

1.04 

0.60 

20  miles  

56 

32.0 

1.60 

34 

19.4 

0.97 

0.60 

25  miles  

64 

36.6 

1.46 

38 

21.6 

0.86 

0.60 

MURPHY.] 


ACTION    OF    AIR    ON    SAIL    OF    AERMOTOR. 


117 


It  will  be  seen  that  the  ratio  of  the  circumference  velocity  of  the 
wheel  to  the  wind  velocity  increases  to  12  miles  an  hour  and  then 
decreases.     In  a  12-mile  wind  the  circumference  of  the  wheel  is  mov- 
ing 1.81  times  faster  than  the  wind  tliat  drives 
it.     It  will  be  seen  also  that  the  circumference      \     \ 
velocitjr  of  the  wheel  when  carrying  the  max-       \     \ 
imum  load  is  about  equal  to  that  of  the  wind        \ 
that  drives  it,  and  that  the  speed  of  the  wheel 
when  carrying  a  maximum  load  is  about  39  per 
cent  less  than  its  speed  when  carrying  no  use- 
ful load. 

ACTION    OF   AIR    ON    THE    SAIL   OF   AN  AER- 
MOTOR. 

It  is  not  our  purpose  to  discuss  this  action 
from  a  theoretical  point  of  view,  but  to  explain 
it  from  the  observed  and  computed  results  of 
the  16-foot  Aermotor.  Fig.  58  shows  the  con- 
cave surface  of  one  sail  of  a  16-foot  Aermotor  in 
a  nearly  horizontal  position  as  it  moves  down- 
ward ;  w  represents  the  velocity  of  the  wind,  and 
v  the  circumference  velocity  of  the  sail.  The 
curve  JAE,  fig.  59,  shows  the  outer  end  of  the 
sail,  and  to,  in  fig.  60,  shows  the  inner  end.  The 

cords  of  these  arcs, 

or  the  plane  of  the 

sail,  makes  an  angle 

(JOP)  of  30°  with 

the    plane    of    the 

wheel.     The  point 

E,  fig.  59,  repre- 
sents a  particle  of 

air  as  it  comes  in    FIG.  58,-san^of  w-foot  Aer- 

contact    with    the 

sail  when  the  wheel  is  carrying  its  best 
load;  EF  represents  the  velocity  of  the 
wind,  EH  the  velocity  of  this  point  of  the 
sail ;  then  EG,  the  other  side  of  the  paral- 
lelogram constructed  on  EH  and  EF,  is 
the  velocity  of  this  particle  of  air  over  the 
sail;  EG  is  not  tangent  to  the  sail.  The 
point  A  represents  a  particle  of  air  as  it 
comes  in  contact  with  the  moving  sail, 
when  the  mill  is  carrying  no  load;  AC 
represents  the  relative  velocity  of  the  particle  of  air.  It  will  be  seen 
that  the  air  does  not  enter  the  sail  tangent  to  it,  but  more  nearly 
tangent  for  best  load  than  for  no  load. 


FIG.  59.— Outer  end  of  sail  of  10-foot 
Aermotor. 


118 


THE    WINDMILL. 


[NO.  42. 


Iii  fig.  60  t  represents  a  particle  of  air  as  it  strikes  the  inner  .end  of 
the  sail  when  the  mill  is  carrying  no  load,  and  a  represents  a  particle 
of  air  as  it  strikes  the  inner  end  of  the  sail  when  the  mill  is  carrying 
its  maximum  load.  It  will  be  seen  that  the  air  does  not  strike  the  sail 
tangent  to  it  at  any  place  for  any  load,  but  that  it  is  most  nearly  tan- 
gent at  the  outer  end  of  the  sail  at  maximum  load.  In  order  for  the  air 
to  enter  the  sail  tangent  to  it  at  maximum  load,  the  angle  POJ  should 

be  a  little  greater  than  30°  at  the  outer 
end,  and  considerably  greater  than  30°  at 
the  inner  end.  As  the  load  is  decreased 
the  angle  POJ  should  be  decreased. 

USEFUL  WORK  OF  TWO  POWER  MILLS 
IN  A  GIVEN  TIME. 

We  can  find  the  useful  work  of  the  12- 
foot  and  the  16-foot  Aermotors  in  a  year, 
as  we  have  for  two  pumping  mills  (pp.  69- 
71).  For  this  purpose  we  will  use  the 
mean  wind  movement  at  Dodge,  Kansas, 
from  1889  to  1893,  as  given  by  Mr.  Willis 
L.  Moore,  Chief  of  Weather  Bureau.1 
The  mean  number  of  hours  per  month 
that  the  wind  velocity  was  0  to  5,  6  to  10, 

etc.  miles  an  hour  at  this  place  is  given  in  the  following  table,  also 
the  mean  horsepower  of  these  two  mills  for  each  month.  The  num- 
ber of  horsepower  hours  for  each  mill  each  month  is  given  at  the 
bottom  of  the  table.  The  horsepower  hours  for  any  month  are 
found  by  multiplying  the  number  of  hours  by  the  horsepower  and 
adding  the  products. 

Table  showing  useful  work  of  12-foot  and  16-foot  Aermotors  in  a  year. 


r 


FIG.  60.— Inner  end  of  sail  of  16-foot 
Aermotor. 


Month. 

Mean  wind  movement  at  Dodge,  Kansas, 
1889-1893. 

Total 
hours. 

Horsepower 
hours. 

Oto5 
miles. 

6  to  10 
miles. 

11  to  15 
miles. 

16  to  20 
miles. 

21  to  25 
miles. 

26  to  30 
miles. 

31  + 

miles 

12-foot 
mill. 

16-foot 
mill. 

January  

Hrs. 
200.9 
176.0 
126.5 
115.2 
119.0 
122.4 
141.4 
178.6 
165.6 
208.3 
194.4 
186.0 

Hrs. 
253.0 
230.1 
208.3 
172.8 
193.5 
187.2 
215.8 
230.6 
180.0 
230.6 
266.4 
267.9 

Hrs. 
156.2 
128.6 
178.6 
158.4 
171.1 
136.8 
178.6 
156.3 
151.2 
141.4 
129.6 
141.4 

Hrs. 
74.4 
74.4 
119.0 
115.2 
119.0 
108.0 
119.0 
96.7 
93.6 
74.4 
64.8 
81.8 

Hrs. 
37.2 
40.6 
59.5 
72.0 
74.4 
86.4 
59.5 

eo.s 

72.0 
52.1 
36.0 
44.6 

Hrs. 
14.9 
20.3 
29.8 
43.2 
37.2 
50.4 
22.3 
14.9 
36.0 
22.3 
14.4 
14.9 

Hrs. 

7.4 
6.8 
22.3 
43.2 
29.8 
28.8 
7.4 
7.4 
21.6 
14.9 
14.4 
7.4 

744 
677 
744 
720 
744 
720 
744 
744 
720 
744 
720 
744 

250.5 
251.6 
386.6 
461.2 
433.  9 
452.0 
339.8 
297.5 
379.6 
294.0 
244.9 
262.2 

358.0 
361.5 
558.9 
671.3 
629.4 
658.2 
489.3 
427.6 
550.  5 
423.5 
350.9 
374.6 

March.  

April 

May  

June 

July 

August  

September 

October  

November 

December  

Mean  

337.8 

487.8 

Horsepower  16- 
foot  mill 

0.13 
0.10 

0.56 
0.41 

1.25 
0.85 

2.00 
1.36 

;}.  15 

2.12 

Horsepower  12- 
foot  mill 

1  Some  Climatic  Features  of  the  Arid  Region,  by  Willis  L.  Moore.     Washington,  1H1H5. 


MURPHY.]  MATHEMATICAL    DISCUSSION.  119 

The  work  done  by  these  mills  is  greatest  at  this  place  in  April 
(401  horsepower  hours  for  the  12-foot  and  671  horsepower  hours  for  the 
16-foot)  and  least  in  November  (245  horsepower  hours  for  the  12-foot 
and  oo  1  horsepower  hours  for  the  16-foot).  The  mean  monthly  power 
is  338  for  the  12-foot  mill  and  488  for  the  16-foot  mill.  Stating  these 
results  in  another  way,  we  may  say  that  the  12-foot  mill  at  this  place 
will  furnish  on  an  average  1.3  horsepower  10  hours  a  day  for  26  days 
a  month,  and  the  16-foot  mill  will  furnish  1.9  horsepower  10  hours  a 
day  for  26  days  a  month.  It  must  be  remembered  that  the  wind 
velocity  on  the  Great  Plains  is  considerably  greater  than  in  the  east- 
ern part  of  the  United  States,  and  that  consequently  the  horsepower 
hours  of  these  mills  when  used  in  New  York  State,  for  example,  will 
be  considerably  less  than  those  given  in  the  foregoing  table. 

MATHEMATICAL  DISCUSSION  OF  TESTS  OF  JUMBO  MILL  NO.  55. 

On  page  46  we  have  given  the  results  of  tests  of  a  15.5-foot  Jumbo 
mill  working  two  6-inch  pumps.  In  order  more  fully  to  deter- 
mine the  power  of  this  mill  and  its  variation  with  the  number  and 
size  of  the  sails,  we  have  had  constructed  mill  No.  55,  shown  in 
PI.  XVI,  B.  It  is  made  of  wood,  the  parts  being  fastened  together 
with  bolts.  The  diameter  is  7.75  feet;  length  of  sails,  11-J-  feet.  There 
are  8  sails,  each  made  of  two  boards  11^  feet  long  and  8  inches  wide. 
There  is  no  governor  or  other  method  of  regulating  the  speed  of  the 
mill  at  high  wind  velocities,  as  in  other  mills,  but  there  is  a  large  door 
or  shield  on  each  side.  By  opening  these  the  mill  may  be  stopped. 
The  mill  is  not  fastened  to  the  ground,  but  may  be  moved  around  by 
hand  so  that  the  wind  strikes  the  sails  at  right  angles.  The  shaft  is 
4  by  4  inches  and  14  feet  long,  carefully  turned  down  in  a  lathe  to  a 
diameter  of  3  inches  near  each  end.  The  friction  brake  is  of  wood, 
has  an  arm  about  3^  feet  long,  and  is  made  so  as  to  fit  on  the  end  of 
the  shaft.  Oil  was  freely  used  on  the  brake.  It  was  not  found  practi- 
cable to  use  loads  greater  than  about  6  pounds  on  a  35-inch  arm,  as 
the  friction  burned  the  shaft;  but  the  results  for  the  four  loads  used 
showed  that  up  to  the  maximum  load  the  speed  of  the  wheel,  or  the 
number  of  revolutions  per  minute,  varies  directly  as  the  load,  so  that 
we  can  easily  compute  the  load  and  speed  for  maximum  power  in  any 
wind  velocity.  The  weight  of  the  wheel  with  its  8  sails  was  about  450 
pounds.  The  coefficient  of  axle  friction  for  well-oiled  yellow  pine  is 
probably  about  0.10,  so  that  the  axle  friction  was  about  45  pounds. 
This  weight  (45  pounds),  acting  with  a  1^-inch  arm,  is  equivalent  to 
about  2  pounds  applied  on  the  brake  with  a  35-inch  arm.  The  friction 
on  starting  is  probably  50  to  100  per  cent  greater  than  the  friction  of 
motion.  The  0  brake  load  then  really  corresponds  to  a  brake  load 
of  2  or  more  pounds. 

Four  sets  of  tests  were  made  of  this  mill,  numbered  1,  2,  3,  and  4. 
In  the  first  set  the  full  sail  area  of  8  sails,  each  11^  feet  by  16  inches, 


120 


THE    WINDMILL. 


[NO.  42. 


was  used.  The  number  of  revolutions  of  the  wheel  for  the  four  brake 
loads  of  0,  1.75,  2.5,  and  4.5  pounds  was  determined  for  velocities  from 
7  to  22  miles  an  hour.  In  the  second  set  of  tests  there  were  8  sails, 
each  having  an  area  of  11|  feet  by  8  inches;  that  is,  each  sail  was 
only  half  as  wide  as  those  used  in  the  first  set  of  tests.  In  the  third 
set  of  tests  the  sail  area  consisted  of  4  sails,  each  11|  feet  by  16 
inches;  that  is,  every  other  full  sail  was  removed.  The  fourth  set  of 
tests  was  made  to  determine  the  effect  of  concentrating  the  air  on  the 
sails  and  reducing  the  resistance  due  to  air  striking  the  shield  and 
glancing  upward  by  the  use  of  an  inclined  surface  of  approach  to 

wheel.      This   inclined 

VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

10  >5  °0  '?5 


Q 
£0* 


£ 
O   W 


FIG.  61.—  Diagram  showing  revolutions  of  wind  wheel  of  mill 
No.  55—  7.  75-  foot  Jumbo.  Curve  marked  0  is  for  no  brake 
load;  curve  marked  4£  is  for  a  brake  load  of  4.5  pounds. 


surface  had  a  length  of 
7  feet  and  formed  an 
angle  of  11°  with  the 
horizontal. 

Test  No.  ./.—In  PL 
XVI,  B,  the  mill  is 
shown  with  8  sails,  each 
11-j-  feet  by  16  inches. 
Fig.  61  shows  the  num- 
ber of  revolutions  of 
the  wheel  per  half  mile 
of  wind  for  two  loads — 
0  and  4.5  pounds — on  a 
35-inch  arm,  for  the 

wind  velocities  shown.  These  curves  for  a  mill  without  any  means  of 
governing  in  high  velocities  are  given  for  comparison  with  curves  of 
mills  having  a  governor.  It  will  be  seen  that  these  curves  are  nearly 
horizontal  straight  lines  beyond  the  point  of  maximum  revolutions 
per  half  mile.  Thus,  for  no  brake  load  the  revolutions  at  12  miles  are 
about  62,  and  at  25  miles  about  59.  In  a  mill  with  a  governor,  as,  for 
instance,  that  shown  in  fig.  36,  the  curve  is  more  inclined,  or  the  drop 
in  the  number  of  revolutions  is  greater. 

Fig.  62  shows  the  number  of  revolutions  per  minute  for  several 
loads,  fig.  63  shows  the  horsepower. 
The  results  of  these  tests  are  as  follows : 

Results  of  tests  of  Jumbo  mill  No.  55  with  8  sails  11\  feet  by  10  inches. 


Load 
on 
brake. 

Load 
per  rev- 
olution 
of  wind 
wheel. 

Revolutions  of  wind  wheel  per 
minute  at  given  wind  veloci- 
ties (per  hour). 

Horsepower  at  given  wind  velocities 
(per  hour). 

I 

i 

co 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

8  miles. 

| 

a 

M 

It)  miles. 

20  miles. 

25  miles. 

Lbs. 
0 
1.75 
2.5 
4.5 

Ft.-lbs. 
0 
32.0 
45.8 

KJ.  5 

11 

24 
22 

20 
17 

,33 
30 
88 
tt 

41 
38 
36 
88 

49 
45 
43 
40 

0.022 
0.028 
0.043 

0.  030 
O.IK!) 
0.063 

().«»{ 
(1.050 
0.082 

0.043 
0.060 
0.100 



U.  S.  GEOLOGICAL  SURVEY 


WATER-SUPPLY  PAPER  NO.  42   PL.  XVI 


A.     VIEW   OF   MILL   NO.   57— 24-FOOT   LITTLE  GIANT. 


B.     VIEW   OF    MILL   NO.   55— 7J-FOOT  JUMBO. 


MURPHY.] 


MATHEMATICAL    DISCUSSION. 


121 


10 


15 


20 


From  these  results  it  is  seen  that  the  reduction  in  the  number  of 
revolutions  per  minute  is  proportional  to  the  load.  For  example,  in  a 
20-mile  wind  a  4^-pound  load  reduces  the  number  of  revolutions  from 
41  to  34,  or  1. 75  revolutions  per  brake  pound.  The  power  =  In  RnL  -r- 
33,000,  where  n  =  the  number  of  revolutions  of  the  wheel  per  minute, 
L  =  the  load  on  brake,  in  pounds,  R  =  the  arm  of  brake  (35  inches), 
n  =  3.1416,  and  33,000  =  the  number  of  foot-pounds  per  minute  in  a 
horsepower.  We  may  write  the  power  thus:  P  =  KnL,  and  compute 
its  value  as  follows,  K  being  a  constant  equal  to  2?rR  ->  33,000: 

P0  =  K  X  41  (revolutions)  X  0  (L)  =  0 
P,  =  K  X  33  (revolutions)  X  4.5  (L)  =  U8.5K. 
P2  =  #X26  (revolutions)  X  8.5  (L)  =  221.0K. 
P3  =  K  X  22.5  (revolutions)  X  10.5  (L)  =  236.3#. 
P4  =  K  X  20.75  (revolutions)  X  11.4  (L)  =  238.6  tf. 
P5  =  K  X  19  (revolutions)  X  12.5  (L)  =  237.5K. 

P4  is  seen  to  be  larger  than  any  of  the  other  values  of  P,  and  gives 
an  approximate  value  of  the 

VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

power  of  the  mill  for  that  wind 
velocity  (20  miles). 

We  may  find  a  more  accurate 
value  in  an  easier  way.  Let  x 
be  the  load  for  maximum  horse- 
power in  any  given  wind  veloc- 
ity. We  have  seen  that  1  pound 
of  load  reduces  the  speed  by 
1.75  revolutions.  Then  we  can 
write  P=K  (41-1.75aj)  (x). 
For  a  maximum  value  of  P  we 
must  differentiate  P  with  re- 
spect to  x,  place  the  first  differ- 
ential coefficient  0,  and  solve 
for  x.  This  value  of  x,  accord- 
ing to  calculus,  makes  the  power 
a  maximum.  Differentiating, 
we  have  P  4-  dx  =  41—2  (1.75oj) 
=  0.  Solving  for  x  we  have 
J5  =  11.7  pounds.  The  corre- 
sponding value  of  the  revolu- 
tions of  the  wheel  per  minute  is  41  — 1.75  x  11.7  =  20.5  revolutions. 

For  a  25-mile  wind  we  have  x  =  49  -^-  3.5  =  14  pounds,  and  -n  — 16.5. 
In  a  similar  way  we  get  the  load  and  revolutions  for  maximum  power 
IBB  42—01 ± 


o   20 


10 


FIG.  62.— Diagram  showing  revolutions  of  wind 
wheel  of  mill  No.  55— 7.75-foot  Jumbo.  Curves 
marked  0,  If,  £4,  and  4£  are  for  brake  loads  of 
0, 1.75,  2.5,  and  4.5  pounds,  respectively;  AB  is 
for  best  load. 


122 


THE    WINDMILL. 


[NO.  12. 


for  other  wind  velocities.     These  and  the  corresponding  horse  powers 
are  as  follows: 

Values  for  the  curve  DK  (maximum  power)  fig.  63. 


Wind 

Revolu- 

velocity 

Load  in 

tions  of 

Horse- 

(miles pei- 
hour). 

pounds. 

wind  wheel 
per  minute. 

power. 

8 

3.1 

6.0 

0.010 

12 

7.0 

12.0 

0.046 

16 

9.4 

16.5 

0.086 

20 

11.7 

20.5 

0.  133 

25 

14.0 

^4.5 

0.190 

The  curve  DK  is  nearly  a  parabola.     The  revolutions  per  minute 
for  the  best  load  are  seen  to  be  very  nearly  equal  to  the  wind  velocity 


VELOCITY  OF  WIND  IN  MILES  PEB  HOUR. 

10  15  20  25 


.20 


.M 


.04 


PIG.  63.— Diagram  showing  horsepower  of  mill  No.  55— 7.75-foot  Jumbo.  The  curves  show  the 
horsepower  for  brake  loads  of  1.75,  2.5,  and  4.5  pounds,  respectively;  dotted  curve  DK  shows 
maximum  power. 

in  miles.     These  are  platted  in  fig.  62,  giving  the  line  AB,  which  is 
nearly  straight. 


RELATION   BETWEEN  WIND  VELOCITY  AND   CIRCUMFERENCE  VELOCITY 

OF  WHEEL. 

If  we  multiply  the  number  of  revolutions  of  the  wind  wheel  for  any 
wind  velocity  by  24.4  feet  (the  circumference  of  the  wheel)  and  divide 
by  the  wind  velocity,  in  feet  per  second,  we  have  the  followii  g  results 
for  no  brake  load  and  for  best  load : 


MURPHY.)  MATHEMATICAL    DISCUSSION.  123 

Table  showing  ratio  between  wind  velocity  and  circumference  velocity  of  wheel. 


Load. 

Wind  velocity  per  hour. 

8  miles. 

12  miles. 

16  miles. 

20  miles. 

25  miles. 

No  load 

0.38 
0.21 

0.55 
0.27 

0.57 

0.28 

0.57 

0.28 

0.55 
0.27 

Best  load 

From  this  we  see  that  the  velocity  of  the  circumference  of  the  wheel 
is  not  more  than  57  per  cent  of  the  velocity  of  the  wind.  For  veloci- 
ties above  a  certain  amount  it  remains  nearly  constant  for  any  load. 
It  will  be  seen  too  that  the  speed  of  the  wheel  for  best  load  is  almost 
exactly  half  that  for  no  brake  load. 

Test  No.  2. — Sail  area,  11-j-  feet  by  8  inches — each  inner  half  sail 
removed.  The  results  of  this  set  of  tests  are  as  follows : 

Results  of  tests  of  Jumbo  mill  No.  55,  with  8  sails  11%  feet  by  8  inches. 


Load. 

Revolutions  of  wind  wheel  per 
minute  at  given  wind  veloci- 
ties (per  hour). 

Horsepower  at  given  wind  velocities 
(per  hour). 

8  miles. 

12  miles. 

16  miles. 

8 

25  miles. 

8  miles. 

12  miles. 

s 

a 

8 

25  miles. 

Pounds. 
0 
3.25 

Ft.-lbs. 
0 
59.6 

9 

22 
17 

30 
26 

39 
32 

47 
40 

0.031 

0.047 

0.058 

0.072 

By  comparing  these  results  with  those  of  test  No.  1  it  will  be  seen 
that  the  number  of  revolutions  per  minute  for  no  load  is  from  two  to 
three  times  less  when  the  half  sails  are  used.  The  3^-pound  load  with 
half  sails  gives  about  the  same  speed  as  the  4^-pound  load  with  whole 
sails.  The  weight  of  the  wheel  is  reduced  about  40  per  cent,  which 
makes  the  reduction  in  speed  less  than  it  would  be  if  the  weight  of  the 
wheel  remained  constant.  It  will  be  seen,  then,  that  for  this  size  of 
wheel  very  little  power  is  gained  by  the  use  of  the  inner  8-inch  board 
of  each  sail.  It  is  quite  likely  that  sails  12  inches  wide  would  give 
fully  as  much  power  as  sails  16  inches  wide. 

Test  No.  3. — The  sail  area  was  4  sails,  each  11-j-  feet  *by  16  inches — 
every  other  full  sail  removed.  The  results  of  this  set  of  tests  were 
almost  the  same  as  those  of  test  No.  1.  There  was  no  measura- 
ble reduction  in  the  speed  of  the  wheel  when  every  other  full  sail  was 
removed.  The  weight  of  the  wheel  was  reduced  about  40  per  cent, 
and  consequently  the  friction.  The  gain  in  pressure  on  the  extra 
sail  area  is  counterbalanced  by  the  additional  friction. 

Test  No.  4- — The  sail  area  was  8  sails,  each  11-j-  feet  by  16  inches — 
the  same  as  for  test  No.  1.  There  was  an  inclined  surface  (shown  in 
PL  XVI,  B}  for  concentrating  air  011  sails  and  in  a  measure  prevent- 


124 


THE    WINDMILL. 


[NO.  42. 


ing  an  upward  current  from  the  front  shield.  The  results  of  this  set 
of  tests  are  the  same  as  those  of  No.  1.  There  was  no  measurable 
increase  in  the  number  of  revolutions  when  the  mill  was  loaded  or 
unloaded,  or  when  the  incline  was  used  or  not  used. 

For  this  size  of  mill  4  sails  each  12  inches  wide  give  the  maximum 
power.  From  our  tests  of  other  mills  we  should  say  that  the  sail 
width  should  increase  directly  as  the  diameter  increases.  For  diam- 
eters of  12  feet  or  more  it  is  likely  that  the  addition  of  one  or  two 
more  sails,  say  5  for  a  12-foot  mill  and  6  for  a  16-foot  mill,  may 
increase  the  power  over  that  for  4  sails. 

In  1895  we  made  some  measurements  of  the  pressure  of  air  on  small 
curved  surfaces,1  from  which  we  infer  that  if  galvanized-iron  sails 
curved  to  a  radius  about  twice  the  width  and  with  the  concave  sur- 
face to  the  wind  were  used  the  power  of  the  mill  would  be  increased 
about  15  per  cent  over  that  with  the  plane  fans. 

Putting  the  results  of  these  tests  of  Jumbo  mills  in  the  most  prac- 
tical form,  we  have  the  following  as  the  proper  sail  area  and  the 
probable  horsepower  of  wooden  Jumbo  mills  in  a  16-mile  wind  when 
properly  loaded,  assuming  the  power  to  increase  as  the  square  of  the 
diameter: 

Table  showing  proper  sail  area  and  probable  horsepoiver  of  Jumbo  wooden  mills  in 

a  16-mile  ivind. 


Diameter  of  wheel. 

Number  of 
sails. 

Width  of 
sails. 

Length  of 
sails. 

Horsepower. 

8  feet 

4 

Inches. 
12 

Feet. 
12 

0  09 

12  feet 

5 

18 

12 

0.20 

16  feet 

6 

24 

12 

0.36 

20  feet                 .     .  . 

6 

30 

12 

0.56 

The  formula  used  for  computing  the  pressure  on  a  series  of  plane 
surfaces  moving  in  the  direction  of  the  velocity  of  the  wind  is — 


In  this  F  is  the  area,  in  square  feet,  of  the  vane,  r  the  heaviness 
of  air  at  the  observed  temperature  and  barometric  pressure,  c  the 
velocity  of  wind,  and  v  the  velocity  of  wind  wheel,  each  in  feet  per 
second. 

The  heaviness  of  the  air  is  found  from  the  formula  — 

B  To 


In  this  To  is  the  absolute  temperature  in  centigrade  degrees. 


1  Kansas  University  Quarterly,  Vol.  IV,  July,  1895. 


MURPHY.]  MATHEMATICAL    DISCUSSION.  125 

29     273 
From  equation  b  we  have  r =0.08X30X30^=0. 07  pound  per  square 

foot.  From  the  table  on  page  123  it  will  be  seen  that  for  maximum 
power  in  a  16-mile  wind  v=0.2Sc.  Substituting  in  equation  a  we  have, 
for  the  pressure  on  one  sail — 

P=11.5X^X0.07  (1-0.27)2  c2=4.1  pounds. 

The  arm  of  this  pressure  about  the  axis  of  the  wheel  is  about  3.06 
feet.  Hence  the  moment  of  this  force  is  4.1x3.6=14.76  foot-pounds. 
This  moment  is  equal  to  the  moment  of  the  brake  load,  and  we  have 
14.76=35^,  and  #=4.24  pounds.  The  load  actually  carried  on  the 
brake,  including  friction,  is  about  8  pounds;  hence  nearly  half  of  the 
working  pressure  comes  from  wind  pressure  on  the  approaching  and 
receding  sails,  or  only  a  little  more  than  half  the*  pressure  comes  from 
the  sail  which  is  at  the  highest  position  possible. 

MATHEMATICAL  DISCUSSION   OF  TESTS  OF  LITTLE  GIANT  MILL 

NO.  56. 

This  is  a  4.67-foot  mill  made  by  Mr.  C.  Hunt,  of  Wichita,  Kansas. 
These  mills  are  made  in  sizes  from  4  to  24  feet  in  diameter,  to  rest  on  a 
low  tower  or  on  a  building.  The  largest  one  yet  built  is  shown  in  PI. 
XVI,  A.  It  is  used  for  grinding  wheat.  The  Little  Giant  mill  will 
be  seen  to  resemble  the  Jumbo  in  that  the  wind  wheel  moves  in  the 
direction  of  the  wind  and  not  across  it.  It  differs  from  the  Jumbo,  how- 
ever, in  having  a  vertical  axis  and  many  curved  iron  sails,  instead  of 
a  horizontal  axis  and  few  plane  wooden  sails.  The  wind  is  prevented 
from  striking  the  sails  as  they  come  around  toward  the  wind  by  a 
shield  which,  when  closed,  covers  about  one-third  of  the  circumfer- 
ence. The  shield  can  move  freely  about  the  axis  of  the  mill  and  has 
hinged  to  it  a  wing  which  can  be  held  at  right  angles  to  the  circum- 
ference. There  is  also  a  vane  fastened  to  the  shield,  to  aid  in  the 
government  of  the  mill.  When  the  wing  of  the  shield  is  closed,  the 
vane  takes  the  direction  of  the  wind  and  places  the  shield  directly  in 
front  of  the  wind  wheel,  shutting  off  the  wind  from  the  wheel. 
When  the  wing  is  open,  the  pressure  of  the  wind  against  it  carries 
the  shield  around,  admitting  the  wind  to  one-half  of  the  wheel.  By 
properly  placing  the  vane  and  using  the  proper  weight  on  the  wing, 
the  wind  is  admitted  to  a  small  or  a  large  portion  of  the  wheel,  and 
thus  the  speed  of  the  wheel  is  regulated.  The  mill  receives  the  wind 
from  all  directions  and  regulates  automatically. 

Mill  No.  56  has  24  curved  iron  sails,  each  3  feet  10£  inches  long  and 
6£  inches  wide,  set  at  an  angle  of  27°  to  the  radius.  The  radius  of 
curvature  of  the  sails  is  7-j-  inches.  The  vertical  shaft  of  the  wind 
wheel  has  a  beveled  cogwheel,  which  gears  into  another  beveled  cog- 
wheel on  a  short  horizontal  shaft.  The  latter  has  a  pitman  for  work- 
ing a  pump.  The  horizontal  shaft  on  which  the  brake  was  placed 


126 


THE    WINDMILL. 


[xo.42. 


was  geared  back  43-f-13.  The  6rake  arm  was  2  feet  1O£  inches  long. 
The  number  of  revolutions  per  minute  of  the  brake  shaft  was  found 
for  the  four  loads  0,  2,  4,  and  6  pounds,  respectively.  The  corre- 
sponding speed  of  the  wind  wheel  is  found  by  multiplying  by  3£. 
The  results  of  the  tests  were  as  follows: 

Results  of  tests  of  Little  Giant  mill  No.  56. 


Load. 

Revolutions  of  brake  shaft  per 
minute  at  given  wind  veloci- 
ties (per  hour). 

Horsepower  at  given  wind  velocities 
(per  hour). 

I 

1 

oo 

12  miles. 

16  miles. 

I 

1 

8 

25  miles. 

8  miles. 

12  miles. 

16  miles. 

! 

25  miles. 

Pounds. 
0 
2 
4 
6 

Ft.-lbs. 
0 
35.7 
71.4 
107.1 

10 
6 

19 
16 
11 
6 

"  25 
21 
18 
14 

31 

27 
23 
19 

38 
34 
30 
26 

0.007 

0.017 
0.024 
0.019 

0.023 
0.039 
0.045 

0.030 
0.050 
0.062 

0.040 
-    0.065 
0.084 

VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

10  15  20  25 

40 


Referring  to  fig.  64,  the  mill  will  be  seen  to  start  for  no  load  in  a 

light  wind — about  5  miles  an 
hour.  More  than  half  of  each 
speed  curve  is  a  nearly  straight 
line.  This  is  due  to  failure  to 
govern,  the  mill  being  held  wide 
open  all  of  the  time.  It  will  be 
seen  that  each  pound  of  load 
reduces  the  speed  about  two 
revolutions  per  minute  for  about 
0.67  of  each  curve.  Fig.  65 
shows  the  brake  horsepower  for 
three  loads — 2,  4,  and  6  pounds, 
respectively.  The  curve  DK,  to 
which  these  load  curves  are  tan- 
gent, shows  the  maximum  power 
of  the  mill.  This  curve  passes 
through  the  points  y  (horse- 
power) =0  when  x  (wind  veloc- 


FIG.  64.— Diagram  showing  revolutions  of  wind 
wheel  of  mill  No.  56— 4.67- foot  Little  Giant.  The 
curves  marked  0,  2,  4,  and  6  are  for  brake  loads 
of  0,  2,  4,  and  6  pounds,  respectively. 


ity)=5,  and  7/=0.024  when  x=l2.     Hence,  if  we  assume  this  curve 
DKto  be  a  parabola,  we  have  for  its  equation— 


The  horsepower  from  this  equation  and  from  fig.  65  is  as  follows, 
y'  being  taken  from  fig.  65  : 


MURPHY.]    COMPARISON    OF    LITTLE    GIANT    AND   JUMBO    MILLS. 
Horsepower  of  mill  No.  56  at  given  wind  velocities. 


127 


X 

y 

y' 

5 

0.000 

0.000 

8 

0.008 

0.007 

12 

0.024 

0.024 

16 

0.046 

0.  045 

20 

0.075 

0.065 

It  will  be  seen  that  the  horsepower  of  this  mill  does  not  increase  as 
fast  as  the  square  of  the  wind  velocity.  From  fig.  65  it  will  be  seen 
that  the  2-pound  curve  is  tangent  at  8  miles,  the  4-pound  curve  at  12 
miles,  and  the  6-pound  curve  at  16  miles  an  hour.  Hence  the  load 
for  maximum  power  increases  about  as  the  first  power  of  the  wind 
velocity.  The  speed  of  the  brake  shaft  for  these  loads  is  6,  11,  and 
14  revolutions  per  minute,  respectively.  Hence  the  speed  of  the 
wind  wheel  does  not  increase  as  fast  as  the  first  power  of  the  wind 
velocity.  The  ratios  of  circumference  velocity  of  wind  wheel  to 
wind  velocity  for  no  load  and  for  maximum  load  for  five  wind  veloc- 
ities are  as  follows: 

Table  showing  relation  of  circumference  velocity  of  wind  wheel  to  wind  velocity. 


Wind  velocity 
per  hour. 

No  load. 

Maximum  load. 

Ratio  of 
revolu- 
tions at 
maxi- 
mum load 
to  revolu- 
tions at 
no  load. 

Revolu- 
tions of 
brake 
shaft  per 
minute. 

Circum- 
ference 
velocity 
in  miles 
per  hour. 

Ratio  of 
circum- 
ference 
velocity 
to  wind 
velocity. 

Revolu- 
tions of 
brake 
shaft  per 
minute. 

Circum- 
ference 
velocity 
in  miles 
per  hour 

Ratio  of 
circum- 
ference 
velocity 
to  wind 
velocity. 

8  miles 

10 
19 
25 

31 

38 

5.2 
9.9 
13.0 
16.1 
19.8 

0.65 
0.74 
0.81 
0.80 
0.79 

6 
11 
14 
16 

3.1 
5.7 
7.3 

8.3 

0.39 
0.47 
0.46 
0.42 

0.60 
0.58 
0.56 
0.52 

12  miles     .... 

16  miles  

20  miles  
25  miles   

From  this  we  see  that  for  no  load  the  greatest  circumference  veloc- 
ity is  only  81  per  cent  of  the  wind  velocity.  For  best  load  the  ratio 
is  47  per  cent.  Here  is  the  great  disadvantage  of  these  wheels,  which 
move  in  the  direction  of  the  wind  instead  of  across  it — they  move 
too  slowly.  The  ratio  of  circumference  velocity  to  wind  velocity  in 
an  Aermotor  is  1.75.  This  is  2.16  times  the  greatest  corresponding 
circumference  velocity  of  the  Little  Giant  mill. 

COMPARISON  OF  LITTLE  GIANT  AND  JUMBO  MILLS. 

From  the  following  table  it  will  be  seen  that  the  circumference 
velocity  of  the  Jumbo  is  only  from  0.55  to  0.70  of  that  of  the  Little 
Giant  for  best  load.  The  horsepower  of  the  Jumbo  is  about  1.9  times 
that  of  the  Little  Giant;  the  ratio  of  the  Jumbo  diameters  is  1.67; 


128 


THE    WINDMILL. 


[NO.  42. 


hence  the  ratio  of  the  power  is  a  little  greater  than  that  of  the  diam- 
eters. It  must  be  remembered,  however,  that  the  Jumbo  is  about 
three  times  the  length  of  the  Little  Giant.  For  the  same  sail  lengths 
the  latter  does  1.57  more  work  than  the  Jumbo. 

Comparative  data  of  Little  Giant  and  Jumbo  mills. 


Mill. 

Maximum  horsepower  at  given 
wind  velocities  (per  hour). 

Circumference  velocity  for 
maximum  load  at  given 
wind  velocities  (per  hour). 

8  miles. 

13  miles. 

16  miles. 

30  miles. 

1 
1 
g 

8  miles. 

13  miles. 

1 
1 

?D 

30  miles. 

25  miles. 

7f-foot  Jumbo 

0.  010 
0.007 

0.046 
0.024 

0.086 
0.045 

0.133 
0.066 

0.190 
0.100 

1.7 
3.1 

3.40 
5.70 

4.70 
7.30 

5.80 
8.30 

4|-fbot  Little  Giant  

Ratio  

1.4 

1.9 

1.9 

2.0 

1.9 

0.55 

0.60 

0.64 

0.70 

Taking  into  account  the  difference  in  the  diameters  of  the  wind 
wheels  of  these  mills,  we  may  say  that  the  Little  Giant  will  furnish 
about  2.5  more  power  than  the  Jumbo  for  the  same  diameter  and 
length  of  sail.  The  Jumbo  requires  a  7-mile  wind  to  start  it  with  no 
load;  the  Little  Giant  will  start  with  no  load  in  less  than  a  5-mile 
wind.  The  Jumbo  has  no  means  of  governing;  the  Little  Giant  gov- 
erns easily  and  completely.  The  Jumbo  gets  the  full  pressure  of  the 
wind  when  it  comes  from  two  directions  only;  the  Little  Giant  works 
equally  well  with  the  wind  from  any  direction.  The  Little  Giant  is 
less  likely  to  be  injured  in  a  windstorm  than  the  Jumbo.  The  first 
cost  of  the  Jumbo  is  somewhat  less  than  that  of  the  Little  Giant.  A 
5-foot  Little  Giant  with  stub  tower  can  be  bought  for  about  $15. 

COMPARISON  OF  LITTLE  GIANT  WITH  8-FOOT  AERMOTOR. 

The  efficiency  of  the  pump  and  well  of  Aermotor  No.  5  (for  descrip- 
tion and  results  of  tests,  see  pages  33  and  34,  Part  I)  is  probably 
about  60  per  cent.  For  the  speeds  and  horsepowers  of  these  mills  we 
have  the  following : 

Comparative  data  of  Little  Giant  and  8-foot  Aermotor. 


Revolutions  of  wind 

Load 
per 

wheel   per  minute 
at  given  wind  ve- 
locities (per  hour). 

Horsepower  at  given  wind 
velocities  (per  hour). 

Mill. 

revolu- 
tion of 

Sail 
area. 

• 

wind 

t 

| 

I 

i 

t 

wheel. 

a 

gj 

a 

a 

i 

a 

a 

a 

a 

a 

s 

50 

8 

3 

a 

CD 

8 

8 

Ft.-lbs. 

Sq.ft. 

8-foot  Aermotor  (No. 
5)  ... 

45 

34 

62 

84 

99 

115 

0.084 

0.115 

0.138 

0.158 

4|-foot  Little    Giant 

(No.  56)  

24 

54 

34 

66 

71 

QO 

0.024 

0.039 

0.050 

0.065 

Ratio 

2.76 

1.96 

0.63 

1.82 

1.53 

1.40 

1.25 

3.50 

3.00 

2.43 

MURPHY.]       COMPARISON    OF   LITTLE    GIANT    AND    AERMOTOR. 


129 


VELOCITY  OF   WIND  IN   MILES   PER  HOUR. 

10  15  20  25 


.08 


It  will  be  seen  that  the  sail  area  of  the  Aermotor  is  only  0.63  that 
of  the  Little  Giant,  that  the  wind  wheel  of  the  former  makes  from 
1.25  to  1.82  more  revolutions  per  minute  than  the  latter,  and  that  the 
power  of  the  former  is  from  3.5  to  2.4  times  greater  than  the  power  of 
the  latter.  While  the  sail  area  of  the  Aermotor  is  only  0.63  that  of 
the  Little  Giant,  the  wind  area  of  the  former  is  much  greater  than 
that  of  the  latter.  The  wind  can  not  enter  the  wheel  of  the  Little 
Giant  over  an  area  greater  than  the  radius  multiplied  by  the  length 
of  the  sail,  or  9.1  square  feet.  In  the  Aermotor  the  wind  enters  the 
wheel  over  an  area  equal  to  the  difference  between  the  areas  of  the  two 
circles,  one  having  a  diameter  of  8  feet,  the  other  having  a  diameter 
of  3  feet.  This  wind  area  is  43.2  square  feet.  Hence  the  wind  area 
of  the  Aermotor  is  43.2-:-  9.1  = 
4.75  times  that  of  the  Little 
Giant.  Here  is  the  great  advan- 
tage that  the  Aermotor  has  over 
the  Little  Giant — it  has  only  0. 63 
of  the  sail  area,  and  hence  cost 
less  for  sails,  and  4.75  times 
more  air  strikes  its  sails  than 
strikes  those  of  the  Little  Giant. 
It  will  be  shown  later  that  in  the 
Little  Giant  the  air  acts  on  its 
sails  while  passing  out  of  the 
wind  wheel  as  well  as  while  pass- 
ing into  the  wheel,  and  thus  the 
power  for  the  same  wind  area  is 
greater  in  that  mill  than  in  the 
Aermotor. 

Fig.  66  is  a  diagram  showing 
the  action  of  the  wind  on  the 
sails  of  the  Little  Giant  mill. 
AH,  BK,  etc.,  are  the  curved 
sails.  The  cord  AH  makes  an 
angle  of  27°  with  the  radius  AP.  CD  is  the  shield,  with  the  wing  DE 
open.  Let  Aa  represent  the  direction  and  magnitude  of  the  wind  with 
respect  to  the  earth.  We  have  seen  that  for  maximum  load  the  ratio 
of  the  circumference  velocity  of  the  wheel  to  the  wind  velocity  is 
0.47;  hence  drawing  Ac  tangent  to  the  circumference  Aa  and  equal  to 
0.47  of  Aa,  and  completing  the  parallelogram  on  them,  we  have  Ab 
representing  the  direction  of  the  wind  with  respect  to  the  moving  sail. 
If  we  assume  this  to  be  the  velocity  of  the  air  over  the  sail  (it  is 
somewhat  less  than  this,  since  Ab  is  not  quite  tangent  to  the  sail  at 
entrance),  we  can  construct  the  path  of  a  particle  of  air  with  respect 
to  the  earth.  The  points  1,  2,  and  3  are  on  this  path,  and  L3  gives 
the  approximate  direction  of  the  particle  of  air  through  the  wheel. 
At  L  we  combine  this  velocity  with  the  inner  circumference  velocity 


.04 


.08 


FIG.  65. — Diagram  showing  horsepower  of  mill  No. 
56— 4.67-foot  Little  Giant.  The  curves  marked 
2, 4,  and  6  show  horsepower  for  brake  loads  of  2, 
4,  and  6  pounds,  respectively;  dotted  curve  DK 
shows  maximum  power. 


130 


THE  WINDMILL. 


[NO.  42 


of  the  sail,  giving  the  velocity  Lp  with  respect  to  the  moving  sail. 
This  is  seen  to  make  a  large  angle  with  the  tangent  at  entrance, 
reducing  its  magnitude  somewhat.  L/4  is  approximately  the  absolute 
path  of  the  particle  over  the  sail,  and  4-5  is  the  direction  of  the  parti- 
cle at  exit.  B6  represents  the  absolute  path  of  a  particle  of  air  as  it 
moves  over  the  sail  BK.  This  particle  of  air  passes  through  the 


FIG.  66.— Diagram  showing  action  of  wind  on  sails  of  mill  No.  56— 4.67-foot  Little  Giant. 


wheel  in  the  direction  6-7.  The  path  6-7  of  this  particle  crosses  the 
path  of  the  particle  from  3;  hence  there  is  interference  inside  the 
wheel,  which  prevents  our  tracing  with  accuracy  the  path  of  a  parti- 
cle out  of  the  wheel.  It  is  evident,  however,  that  after  passing  into 
the  wheel  the  air  strikes  the  concave  side  of  the  sails  on  the  opposite 
side,  and  aids  in  pushing  the  wheel  around,  so  all  the  work  is  not  done 
by  the  sails  on  the  side  where  the  air  enters. 


MURPHY.] 


INDICATED    AND   TRUE    VELOCITIES. 


131 


INDICATED   AND  TRUE  VELOCITIES. 

Thus  far  all  of  our  results  for  speed  and  power  of  windmills  are 
given  in  terms  of  indicated  velocities,  that  is,  velocities  as  read  from 
the  Robinson  cup  anemometer.  It  is  necessary,  or  at  least  desirable, 
to  examine  these  to  see  whether  they  agree  with  true  velocities  or  dis- 
tances actually  passed  over  by  the  wind  per  hour.  Fig.  67  shows  the 
Robinson  cup  anemome- 
ter as  used  by  the  United 
States  Weather  Bureau. 
This  instrument  was  in- 
vented in  1846  by  Dr.  T. 
R.Robinson,  of  Armagh, 
Ireland,  and  is  now  used 
by  several  meteorolog- 
ical bureaus  for  the  meas- 
urementof  wind  velocity. 
It  gives  a  continuous  rec- 
ord of  wind  movement 
and  requires  no  device, 
such  as  a  vane,  to  give 
it  the  proper  direction 
with  respect  to  the  wind. 
It  is  made  so  that  each  50 
revolutions  of  the  cups 
can  be  read  on  the  dial, 
and  there  is  an  electrical 
device  for  recording 
each  250  or  each  500  rev- 
olutions of  the  cups. 

Referring  to  fig.  68,  let 
A  —  the  upper  and  B  = 
the  lower  cup  of  a  Robin- 
son anemometer  rotat- 
ing about  the  axis,  let  c 
equal  the  velocity  of  the 
wind,  and  v  the  velocity 
of  the  cup  center,  each  in 
feet  per  second ;  x  =  the 
ratio  of  the  velocity  of 
the  wind  to  that  of  the 
cup  center,  Pl  =  the 
pressure  on  the  concave 


FIG.  67.— Anemometer  and  cups,  c,  spindle  which  forms 
the  axis  of  revolution  of  the  cups;  m,  50-tooth  wheel  which 
engages  an  endless  screw  on  the  end  of  the  spindle;  /,  small 
toothed  wheel  which  engages  an  endless  screw  on  the  axis  of 
the  wheel  m ;  e,  pair  of  dial  wheels  which  are  moved  by  the 
wheel  7;  p,  one  of  ten  contact  pins  to  aid  in  closing  the  electric 
circuit  at  the  end  of  each  mile  of  wind;  p',  two  of  these  pins 
connected,  forming  the  tenth  mill  pin;  ?r,  contact  spring;  q, 
a  contact  point  at  the  end  of  contact  spring;  t,  small  insulated 
tube  connecting  q  with  the  insulated  binding  post  u  and 
with  the  second  binding  post  v. 


surface,  and  P2  =  the 
pressure  on  the  convex  surface  of  the  cup.  Dr.  Robinson  found  from 
sixteen  experiments  with  stationary  cups  exposed  to  wind  of  several 
velocities  that  for  all  velocities  the  pressure  when  the  concave  surface  of 


132 


THE  WINDMILL. 


[NO.  42. 


the  cup  is  toward  the  wind  is  about  four  times  that  when  the  convex  sur- 
face is  presented  to  the  wind.  The  pressure  on  the  moving  cup  A  is 
Pl=KlFr(c—  v)2-t-2gS  and  the  pressure  on  the  cupB\sP2=K2Fr(c+ 
v)2-±-  2g;  F being  the  area  of  the  cup,  K^  and  Kz  being  constants  the  ratio 
of  which,  as  found  by  Robinson,  is  4,  r  the  heaviness  of  air,  and  c+v 
and  c— v  the  relative  velocities  of  the  cups.  Neglecting  friction  in  the 
anemometer,  inertia  of  cups  and  arms,  and  the  influence  of  two  of  the 
cups  until  they  are  near  the  position  shown  in  fig.  68,  we  see  that  for 
uniform  velocity  Pl  must  equal  P2;  if  P1  is  greater  than  P2,  v  will 
increase ;  if  P1  is  less  than  P2,  v  will  decrease.  We  have,  therefore,  for 
uniform  velocity  K^  FT  (c—v)2-:-2g=K2  FT  (v+c)2-r-2g  or  4  (c— v)2= 
(c+v)2.  This  equation  can  be  put  in  the  form  4(^—1  )2=(x+ I)2.  Solv- 
ing we  have  o?=3;  that  is,  the  velocity  of  the  wind  is  three  times  that 
of  the  cup  centers.  For  an  anemometer  having  arms  6.72  inches 
long,  the  distance  passed  over  by  a  cup  center  in  500  revolutions  is 

2x22      6  72 
d=—y—  X  -jg-  X  3  x  500=5,280  feet,  or  1  mile. 

Dr.  Robinson  believed  that  this  ratio  of  wind  velocity  to  that  of 

cup  center  was  true  for 
all  velocities,  and  con- 
sequently the  makers  of 
the  instrument  have 
marked  the  dial  in 
miles.  We  shall  see, 
however,  from  the  rat- 
ing of  the  one  that  we 
have  used  in  these  wind- 
mill tests  that  this  ratio 
is  not  a  constant.  It 
will  be  seen  that  'for 
wind  of  uniform  veloc- 
ity this  ratio  is  a  vari- 
able which  has  the  value 
3  for  9  miles  an  hour,  is 
greater  than  3  for  less 
velocities,  and  is  less 
than  3  for  greater  veloc- 
ities than  9  miles  an 
hour;  in  other  words,  to  get  true  velocities  we  must  add  a  correction 
below  9  miles  an  hour  and  subtract  a  correction  above  that  velocity. 
Friction  and  inertia  were  neglected  in  deriving  the  foregoing  value  of 
this  ratio.  The  former  has  little  influence  in  an  instrument  kept  in 
good  condition,  but  in  a  poorly  kept  instrument  it  may  have  a  large 
influence  for  low  velocities.  This  ratio  has  been  found  to  be  8  to  10 
with  much  friction.  The  inertia  of  the  arms  and  cups  has  a  marked 
influence  on  this  ratio,  especially  for  ordinary  gusty  wind.  As  the 


c 


Fio.  68.— Diagrammatic  section  of  anemometer  cups. 


Church's  Mechanics  of  Engineering,  j>.  815. 


MURPHY.] 


INDICATED    AND    TRUE    VELOCITIES. 


133 


gustiness  of  the  wind  increases  the  correction  to  be  subtracted  to  get 
the  true  velocity  increases  also. 

The  relation  between  the  indicated  and  true  velocity  of  an  anemom- 
eter is  found  by  moving  the  anemometer  in  still  air  at  different 
velocities,  and  noting  the  distance  passed  over,  also  the  readings  of 
the  instrument.  It  is  seldom  that  the  air  out  of  doors  is  still  for  any 
considerable  length  of  time,  so  that  this  comparison  is  usually  made 
within  an  inclosure,  the  anemometer  being  carried  around  in  a  circle. 
The  radius  of  the  whirler  should  be  as  long  as  possible,  and  made  so 
as  to  affect  the  circulation  of  air  as  little  as  possible,  and  to  reduce 
the  effect  of  the  centrifugal  force. 

The  whirling  machine  that  we  have  used  for  rating  the  anemometer 
is  the  property  of  the  United  States  Weather  Bureau.  It  consists 
essentially  of  an  arm  28  feet  long  and  8  feet  above  the  ground,  on  the 
end  of  which  the  anemometer  is  carried  at  an  elevation  of  2  feet  above 
the  arm.  This  arm  is  counterweighted  and  is  stiffened  by  the  rods. 
It  is  clamped  to  a  vertical  shaft,  which  carries  a  cogwheel  near  its 
lower  end.  A  cogwheel  on  a  horizontal  shaft  engages  the  large  cog- 
wheel and  gives  rotation  to  the  arm.  For  low  velocities  the  power 
was  applied  through  a  crank  on  the  horizontal  shaft,  and  for  higher 
velocities  by  a  crank  on  a  second  shaft,  the  latter  working  the  first 
shaft  by  means  of  two  sprocket  wheels  and  a  chain.  The  machine 
was  set  up  out  of  doors,  in  a  sheltered  place  away  from  any  building, 
and  was  used  on  several  nights  when  there  was  scarcely  any  wind. 
It  was  made  to  rotate  about  half  the  time  in  the  positive  direction 
and  the  other  half  in  the  negative  direction. 

A  new  Robinson  anemometer  was  used  with  which  to  compare  results 
obtained  for  the  one  used  in  our  windmill  tests.  The  results  for  these 
instruments  agree  quite  closely.  The  results  obtained  on  December 
29,  when  there  was  no  perceptible  wind,  are  as  follows: 

Table  showing  relation  between  indicated  and  true  velocity  of  anemometer. 


Indicated 
velocity,  in 
miles  per 
hour. 

Revolu- 
tions of 
long  arm 
in  i  mile  of 
wind. 

True  veloc- 
ity, in  miles 
per  hour. 

Correction, 
in  miles. 

Correction, 
in  miles, 
for  gusty 
wind. 

6 

15.5 

6.20 

+  0.20 

0 

8 

15.1 

8.05 

+0.05 

-0.2 

11 

14.7 

10.78 

-0.22 

-0.6 

15 

14.2 

14.20 

-0.80 

-1.2 

20 

13.8 

18.40 

-1.60 

-2.2 

25 

13.53 

22.55 

-2.45 

-3.2 

30 

13.3 

26.60 

-3.40 

-4.3 

It  will  be  seen  that  the  indicated  velocity  is  less  than  the  true 
velocity  for  velocities  less  than  0  miles  an  hour;  above  9  miles  the 
true  velocity  is  less  than  the  indicated  velocity.  In  other  words,  the 
correction  is  added  below  9  miles  an  hour  and  subtracted  above 
that  velocity.  It  will  be  seen  that  up  to  11  miles  an  hour  these 


134 


THE    WINDMILL. 


[MX  42. 


anemometer  readings  differ  very  little  from  the  true  readings,  but 
for  higher  velocities  the  correction  becomes  quite  large.  The  last 
column  of  the  foregoing  table  gives  the  corrections  to  be  applied  to 
the  indicated  velocities  of  the  Weather  Bureau  Robinson  anemometer 
for  gusty  wind.1  The  motion  of  ordinary  moving  air,  when  studied 
with  a  very  light  anemometer  recording  each  revolution,  is  found  to 
vary  suddenly  by  large  amounts.  The  rate  of  motion  changes  20  or 
30  miles  an  hour  in  a  few  seconds.2  The  record  of  the  standard  Rob- 
inson anemometer,  recording  miles  or  half  miles,  does  not  show  these 
sudden  changes,  but  gives  an  average  velocity  for  the  wind.  Its 


VELOCITY   OF   WIND   IN   MILES 
9  11  13  15 


PER  HOUR. 
17  19 


l.r, 

1.4 

L8 


1.1 

II.Q 

2  0.9 


t! 

B  ' 
0  0.7 
M 

|  0.6 
§0.6 


0.4 


Oit 

o.  ] 


7 


4 


FIG.  69.  —  Diagram  showing  horsepower  of  mill  No.  27  —  12-foot  Aermotor.    Curve  AB  shows 
power  for  indicated  velocity,  assuming  wind  to  be  not  gusty;  AD  shows  power  for  true  velocity; 

AE  shows  power  in  average  gusty  wind;  A  F  shows  power  from  H.  P.  = 


weight  and  consequent  inertia  cause  it  to  continue  its  rotation  for  a 
time  after  the  impulse  is  passed,  and  when  the  next  impulse  strikes 
the  cups  their  weight  will  not  allow  them  to  take  the  velocity  of  the 
impulse.  The  less  the  weight  the  more  nearly  will  the  velocity  of 
the  cups  be  that  of  each  gust.  The  effect  is  that  the  cups  revolve 
faster  in  a  gusty  wind  of,  say,  20  miles  an  hour,  than  in  wind  of 
the  same  velocity  but  not  gusty.  Two  difficulties  arise  in  dealing 
with  gusty  wind:  (1)  The  gustiness  of  any  wind  varies  from  time  to 
time,  and  the  anemometer  gives  no  indication  of  it;  (2)  we  have  no 
means  of  producing  artificial  gusty  wind  in  which  to  rate  anemom- 
eters. If  the  anemometer  is  rated  in  natural  wind,  then  a  correction 


1  Anemometry,  by  C.  F.  Marvin.     Washington,  1893. 

3  The  Internal  Work  of  the  Wind,  by  S.  P.  Langley.     Washington,  1893. 


MURPHY.]  COMPARISON    OF    EXPERIMENTS.  135 

must  be  applied,  but  its  amount  is  uncertain.  The  velocity  of  gusty 
wind  can  not,  therefore,  be  measured  with  certainty.  This,  however, 
does  not  lessen  the  value  of  the  Robinson  anemometer  as  an  instru- 
ment for  measuring  wind  velocity,  nor  introduce  an  error  in  our 
results.  For  a  given  velocity  and  gustiness  the  anemometer  will 
always  give  the  same  reading,  and  the  same  gusty  wind  which  strikes 
the  anemometer  strikes  the  windmill  directly  behind  it.  The  diffi- 
culty arises  when  we  try  to  compare  results  in  which  the  Robinson 
anemometer  was  used  in  measuring  velocity  with  those  in  which  some 
other  form  of  anemometer  was  used.  The  corrections  given  in  the 
last  column  of  the  table  were  found  by  Prof.  C.  F.  Marvin,  of  the 
United  States  Weather  Bureau,  and  are  for  ordinary  gusty  wind. 

The  Robinson  anemometer  is  now  so  generally  used  to  measure 
wind  velocity  that  it  is  better  to  express  the  speeds  and  powers  of  wind- 
mills in  terms  of  these  than  of  any  other.  If  results  are  desired  in 
terms  of  true  velocities,  they  can  be  found  approximately  by  means 
of  the  table  of  corrections  given  on  page  133.  Fig.  69  shows  the  power 
of  mill  No.  27  expressed  in  terms  of  three  kinds  of  velocity:  AB 
shows  the  power  assuming  the  wind  to  be  not  gusty;  AD  shows  the 
power  for  true  velocity,  that  is,  after  applying  the  corrections  in  the 
fourth  column  of  the  table;  AE  shows  the  power  in  average  gusty 
wiud,  that  is,  after  applying  the  corrections  in  the  last  column  of  the 
table;  AF would  give  its  power  if  the  power  increased  as  the  cube  of 
the  indicated  velocity. 

COMPARISON    OF   WRITER'S    EXPERIMENTS    WITH    THOSE 

OF   OTHERS. 

Comparison  with  Smeaton' s  experiments. — In  this  comparison  we  use 
indicated  velocities  and  results  for  best  mills.  Smeaton's  results  are 
given  on  pages  15  and  16,  Part  I.  It  will  be  remembered  that  his  wheels 
were  3.5  feet  in  diameter,  moved  against  still  air  in  a  circle  of  5.5  feet 
radius,  and  that  his  wind  velocities  varied  from  3  to  6  miles  an  hour. 

Smeaton  found  (maxim  1,  page  15,  Part  I)  that  the  velocity  of  a  wind- 
mill sail,  whether  loaded,  so  as  to  produce  maximum  power,  or  un- 
loaded, is  nearly  as  the  velocity  of  the  wind.  We  have  found  that 
the  velocity  of  wind  wheel  when  loaded  increases  nearly  as  the  wind 
velocity,  but  when  it  is  unloaded  it  increases  as  the  square  root  of  the 
wind  velocity. 

Smeaton  found  (maxim  3)  that  the  maximum  power  increases  some- 
what less  rapidly  than  as  the  cube  of  the  wind  velocity.  We  have 
found  that  the  maximum  power  increases  as  the  square  of  the  wind 
velocity — for  true  velocities  somewhat  faster  than  as  the  square  of  the 
wind  velocity. 

Smeaton  found  (last  part  of  maxim  5)  that  the  power  for  a  constant 
load  increases  as  the  first  power  of  the  wind  velocity.  Our  experi- 
ments show  that  for  a  constant  load  the  power  increases  as  the  square 
root  of  the  wind  velocity. 


136 


THE    WINDMILL. 


[NO.  42. 


Smeaton  found  (maxim  6)  that  the  circumference  velocities  of  sim- 
ilarly made  mills  of  different  diameters  vary  inversely  as  the  diameters. 
We  have  found  this  to  be  true. 

Smeaton  found  (maxim  8)  that  the  maximum  power  for  similarly 
made  mills  increases  as  the  squares  of  the  diameters.  We  have  found 
that  it  increases  about  as  the  1 . 25  power  of  the  diameters. 

Smeaton  found  (maxim  9)  that  the  circumference  velocity  of  the 
Dutch  sail,  whether  loaded  or  unloaded,  is  considerably  greater  than 
the  wind  velocity.  We  find  that  it  is  nearly  equal  to  the  wind  veloc- 
ity for  loaded  sail,  and  about  1.75  times  the  wind  velocity  for  the 
unloaded  sail. 

Comparison  with  Coulomb's  experiments. — In  this  comparison  indi- 
cated velocities  are  used.  Coulomb's  observations  (see  page  16,  Part 
I)  were  made  on  a  Dutch  mill  (fig.  1,  Part  I)  having  a  wind  wheel 
70  feet  in  diameter.  He  found  that  at  a  wind  velocity  of  about  15 
miles  an  hour  the  wind  wheel  was  making  13  revolutions  per  min- 
ute and  yielding  about  7  horsepower  of  useful  work.  Comparing  this 
with  the  results  for  the  16-foot  Aermotor  for  maximum  load,  we  have 
the  following: 

Comparison  of  results  of  tests  of  Coulomb's  70-foot  mill  with  writer's  16-foot 

Aermotor. 


Mill. 

Revolutions 
of  wind 
wheel  per 
minute. 

Circumfer- 
ence velocity 
in  feet  per 
minute. 

Horsepower. 

70-foot  mill 

13 

2,860 

7.0 

16-  foot  Aermotor          

28 

1,408 

0.8 

The  circumference  velocity  of  the  large  mill  is  more  than  twice  that 
of  the  smaller  one.  The  ratio  of  the  powers  is  7  -i-  0.8  =  8.8.  The  ratio 
of  the  diameters  is  704-16  =  4.4.  The  ratio  of  the  powers  is  about 
twice  that  of  the  diameters.  The  ratio  of  the  squares  of  the  diameters 
is  19. 14. 

It  is  very  likely  that  the  wind  velocity  as  found  by  Coulomb  is  too 
small;  the  very  large  circumference  velocity  of  his  wheel  indicates 
this.  It  is  probable  that  the  wind  velocity  during  his  observations  was 
about  20  miles  an  hour  instead  of  15.  In  a  20-mile  wind  the  horse- 
power of  the  16-foot  mill  is  about  twice  that  in  a  15-mile  wind,  and 
the  speed  34  revolutions  per  minute  against  28.  The  ratio  of  the 
horsepowers  would  then  be  about  as  the  diameters  of  the  wind  wheels. 

Comparison  with  Griffith's  experiment. — The  performance  of  a 
pumping  windmill  depends  on  so  many  factors,  most  of  which  may 
affect  the  result  to  a  large  degree,  that  it  is  doubtful  whether  it  is 
worth  while  to  make  a  comparison  where  the  conditions  differ  much. 
There  is  the  pump  efficiency  alone,  other  conditions  being  the  same, 


MURPHY.] 


COMPAKISON    OF    EXPERIMENTS. 


137 


which  may  make  the  horsepower  of  one  four  or  more  times  that  of  the 
other.  For  example :  Both  mills  have  a  brake  power  of  1  horsepower ; 
one  mill  works  a  pump  which  has  an  efficiency,  under  present  condi- 
tions, of  20  per  cent,  its  useful  horsepower  being  0.2;  the  other  mill 
operates  a  pump  which  has  an  efficiency  of  80  per  cent,  its  horsepower 
being  0.8,  or  four  times  that  of  the  other.  We  have  seen  that  for 
wind  velocities  above  a  certain  amount  the  power  increases  nearly  as 
the  load,  so  that  by  doubling  the  load  for  the  higher  velocities  the 
power  is  doubled.  The  gearing  and  means  of  governing  affect  the 
power  in  a  somewhat  less  degree.  The  way  in  which  the  wind  velocity 
is  measured  may  affect  the  recorded  power  and  speed.  If  the  wind 
wheel,  or  tower,  or  any  other  obstacle  obstructs  the  free  flow  of  the 
air  to  the  anemometer,  the  recorded  velocity  will  not  be  as  great  as  it 
should  be.  If  the  anemometer  is  placed  on  the  platform,  it  will  give 
a  less  velocity  than  if  held  some  distance  in  front  of  the  wheel  and  at 
the  height  of  the  axis.  The  temperature  and  barometric  pressure 
affect  the  power. 

In  Mr.  Griffiths's  data  (see  pages  17  and  18,  Part  I)  the  load  factor 
is  known,  but  the  wind  velocities  he  gives  are  small,  and  for  small 
velocities  it  is  difficult  to  compute  the  effect  on  the  power  of  differ- 
ences in  load.  In  fact,  most  of  his  velocities  are  less  than  are  required 
to  start  irrigating  mills.  Only  four  of  his  mills,  viz,  Nos,  1,  2,  5,  and  6, 
are  comparable  with  mills  that  we  have  tested.  The  mills  with  which 
we  have  compared  them  are  Nos.  36,  38,  and  47 — very  lightly  loaded 
mills  with  low  pump  efficiency. 

Comparison  of  results  of  Griffiths's  tests  with  those  of  writer's  tests. 


Mill. 

Outer  di- 
ameter of 
sail. 

Load  per 
stroke  of 
pump. 

Wind  ve- 
locity. 

Strokes  of 
pump  per 
minute. 

Horse- 
power. 

Feet. 

Ft.-lbs. 

Miles. 

Griffiths's  No.  1  ... 

22.3 

480.0 

7.0 

6.8 

0.098 

Writer's  No.  36  .. 

22.5 

248.0 

7.0 

5.0 

0.038 

Griffiths's  No.  2  . 

11.5 

29.2 

5.8 

13.0 

0.011 

Writers  No.  38  .. 

10.0 

21.0 

5.8 

9.0 

0.006 

Griffiths's  No.  5  .  . 

10.2 

51.0 

8.5 

20.5 

0.028 

Writer's  No.  38  .  . 

10.0 

21.0 

8.5 

21.0 

0.014 

Griffiths's  No.  6... 

9.8 

30.7 

6.0 

12.5 

0.012 

Writer's  No.  47  .  .  . 

10.0 

37.0 

6.0 

7.0 

0.008 

It  will  be  seen  from  this  table  that  the  horsepowers  of  the  mills  tested 
by  Mr.  Griffiths  are  greater  than  the  horsepowers  of  the  mills  we  have 
tested.  The  speeds  of  the  wheels  are  also  greater,  except  in  Nos.  5  and 
38.  We  are  of  the  opinion  that  a  part  of  the  difference  in  results  is 
due  to  difference  in  the  method  of  measuring  the  wind  velocity.  The 
wind  velocity  found  by  Mr.  Griffiths  is  less  than  we  have  found  it. 

Comparison  with  King's  experiments. — Professor  King's  measure- 
ments of  the  brake  horsepower  of  a  16-foot  Aermotor  are  given  on 
IRR 


138 


THE    WINDMILL. 


page  20,  Part  I.  These  results  are  plotted  in  fig.  70,  giving  the  curve 
AB*".f>  The  curve  of  maximum  power  for  the  16-foot  Aermotor  No.  44  is 
redrawn  in  this  figure  as  curve  CD.  It  will  be  seen  that  these  curves 
are  nearly  parallel  to  16  or  17  miles  an  hour,  and  then  diverge  rapidly. 
Believing  that  much  of  this  difference  is  due  to  the  wind  wheel  of 
Professor  King's  mill  interfering  with  the  anemometer,  we  have  experi- 
mented with  two  anemometers,  one  located  29  feet  directly  south  of 
the  wind  wheel  of  mill  No.  44,  the  other  located  27  feet  directly  north 
of  it,  and  each  recording,  side  by  side,  the  wind  velocity  on  an  elec- 
tric register.  The  hourly  wind  velocity  for  fourteen  consecutive 
hours,  during  the  first  ten  of  which  the  mill  was  working  and  during 
the  last  four  of  which  it  was  out  of  the  wind,  is  given  in  the  follow- 
ing table: 

Table  showing  wind  velocities  during  writer's  experiments  with  anemometers  on 

mill  No.  44. 


Hour. 

Direction 
of  wind. 

Wind  velocities. 

Ratio. 

Front  ane- 
mometer. 

Rear  ane- 
mometer. 

First    

SE 

Miles. 
15.0 
18.0 
18.0 
19.5 
18.0 
16.3 
15.2 
12.7 
10.5 
7.7 
7.2 
8.6 
10.5 
10.3 

Miles. 
10.2 
13.4 
13.5 
12.8 
13.5 
12.6 
10.0 
9.6 
7.5 
5.5 
7.2 
8.6 
10.6 
10.4 

Per  cent. 
0.68 
0.74 
0.75 
0.65 
0.74 
0.77 
0.65 
0.76 
0.71 
0.72 
1.00 
1.00 
1.00 
1.00 

Second  _. 

..do.. 

Third 

do 

Fourth 

.      do 

Fifth 

SW  
.  _  do  _  . 

Sixth           .     ... 

Seventh  

S  .. 

Eighth 

SE 

Ninth 

do 

Tenth          

..do    . 

Eleventh           

.-do.. 

Twelfth 

do 

Thirteenth 

.      do    . 

Fourteenth           .             . 

...do 

The  direction  of  the  wind  is  the  mean  for  each  hour,  as  shown  by 
an  anemoscope.  When  the  wind  was  from  the  southeast  it  occasion- 
ally came  for  a  short  time  almost  directly  from  the  east;  and,  again, 
when  from  the  southwest  it  occasionally  came  for  a  time  from  the 
west. 

It  will  be  seen  that  the  hourly  velocity,  27  feet,  behind  the  running 
wheel  was  only  65  to  77  per  cent  of  that  in  front  of  the  wheel.  As 
soon  as  the  wheel  was  turned  out  of  the  wind  the  two  anemometers 
recorded  nearly  the  same  velocity. 

Referring  now  to  the  direction  of  the  wind  when  Professor  King's 
windmill  tests  were  made,  and  remembering  that  his  anemometer  was 
40  feet  directly  east  of  the  moving  wheel,  it  will  be  seen  that  nearly 
all  of  the  tests  were  made  when  the  wind  came  from  the  northwest  or 


MURPHY.] 


COMPARISON    OF    EXPERIMENTS. 


139 


VELOCITY  OF  WIND  IN  MILES  PER  HOUR. 

10  15  20  25 


the  southwest,  and  that  consequently  the  moving  wheel  must  have 
interfered  with  the  proper  working  of  the  anemometer,  causing  it  to 
record  a  less  velocity  than  actually  existed,  and  making  the  horse- 
power greater  than  if  the  anemometer  had  been  in  front  of  the  wheel. 
In  fig.  70  it  will  be  seen  that  an  increase  of  from  5  to  25  per  cent  in 
Professor  King's  wind  velocities  would  move  his  curve  over  to  the 
right  of  our  curve.  These  curves  are  found  in  very  different  ways — 
Professor  King's  from  26  single  observations,  ours  from  more  than  150 
observations.  Instead  of  finding  points  on  this  curve  when  the  proper 
load  is  unknown,  we  have  found  speed  and  power  curves  for  constant 
loads,  and  from  these  drawn  the 
curve  of  maximum  power.  None 
of  the  mills  that  we  have  tested 
have  given  a  power  curve  like 
AB  in  fig.  70.  It  will  be  noticed 
too  that  the  curve  CD  is  quite 
like  the  corresponding  one  for 
the  12-foot  Aermotor.  This  we 
should  expect,  since  the  mills  are 
similar  in  construction. 

Comparison  with  Perry's  ex- 
periments. — Indicated  velocities 
are  used  in  this  comparison. 
Some  of  Mr.  Perry's  results  are 
given  on  pages  20  and  21,  Part  I. 
His  tests  were  made  on  wheels 
5  feet  in  diameter,  carried  against 
still  air  in  a  circle  14  feet  in 
diameter,  and  his  wind  velocities 
were  not  greater  than  about  11 
miles  an  hour.  Mr.  Perry  states 
that  his  results  agree  with  those 
of  Smeaton.  A  comparison  of  our  results  with  Smeaton's  has  been 
given  on  pages  135  and  136. 

We  will  compare  in  detail  the  working  of  two  of  Mr.  Perry's  wheels, 
viz,  Nos.  44  and  48,  with  that  of  our  12-foot  Aermotor  No.  27. 

Mr.  Perry's  wheel  No.  44  is  somewhat  like  the  wind  wheel  of  our 
12-foot  Aermotor  No.  27.  It  has  12  curved  wooden  sails,  each  18  by 
12.3  by  5.8  inches,  having  a  weather  angle  at  the  inner  end  of  sail  of 
30°  and  an  angle  of  25°  at  the  outer  end.  The  air  is  more  obstructed 
in  its  passage  through  this  wheel  than  through  the  wheel  of  No.  27. 
The  following  are  some  of  the  results  for  these  mills  in  an  8.5-mile 
wind,  the  only  velocity  which  Mr.  Perry  gives  for  his  mill. 


HORSEPOWER. 

W  *•  Cr 

B 

1 

1 

GATED 
ts 

1 

/ 

/ 

/ 

g 
i 

// 

<~>* 

x" 

FIG.  70.— Diagram  showing  horsepower  of  two 
16-foot  Aermotors.  Curve  AB  shows  brake 
horsepower  of  Professor  King's  16-foot  Aer- 
motor; CD  shows  maximum  power  of  writer's 
16-foot  Aermotor  No.  44. 


140 


THE    WINDMILL. 


[NO.  42. 


Comparison  of  results  of  tests  of  Perry's  5-foot  mill  No.  44  with  -writer's  tests  of 

12-foot  Aermotor  No.  27. 


Mill. 

Area 
of  sail. 

Wind 
veloc- 
ity. 

Load 
per 
revolu- 
tion. 

Maximum  load. 

Horse- 
power. 

No  load. 

Revolu- 
tions per 
minute. 

Circum- 
ference 
velocity. 

Revolu- 
tions per 
minute. 

Circum- 
ference 
velocity. 

Perry's  mill  No.  44.  . 
12-foot     Aermotor 
No.  37     

*WS 

73.0 

Miles. 

8.5 

8.5 

Ft.-lbs. 
11.3 

22.2 

44.4 
19.0 

8.6 
11.9 

0.016 
0.13 

84.3 
32.5 

22.1 
20.4 

Ratios  

5.3 



19.6 



1.38  I    8.12 

0.92 

It  will  be  seen  that  the  load,  ID  foot-pounds,  per  revolution  of  wind 
wheel  is  19.6  times  greater  and  the  circumference  velocity  for  maxi- 
mum load  is  1. 38  times  greater  for  No.  27  than  for  the  5-foot  wheel,  but 
that  the  circumference  velocity  for  no  load  is  a  little  less  for  No.  27 
than  for  the  other  mill.  The  power  of  the  12-foot  Aermotor  is  more 
than  8  times  that  of  the  5-foot  mill,  and  its  sail  area  is  5.3  times 
greater. 

'  We  will  next  compare  the  12-foot  Aermotor  No.  27  with  Mr.  Perry's 
5-foot  mill  No.  48,  which  gave  the  greatest  power  of  the  61  wheels  tested 
by  him.  It  had  six  curved  pasteboard  sails,  each  19  by  23.7  by  10.9 
inches,  set  at  a  weather  angle  of  35°  at  the  inner  end  of  the  sail,  and 
at  an  angle  of  25°  at  the  outer  end.  All  obstructions  to  the  free  flow 
of  air  over  the  back  of  the  sails  were  removed.  The  following  are 
some  of  the  results  for  these  mills  at  a  wind  velocity  of  11  miles  an 
hour : 


Comparison  of  results  of  tests  of  Perry's  5-foot  mill  No. 

12-foot  Aermotor  No.  27. 


ivitli  writers  tests  of 


Mill. 

Area 
of  sail. 

Wind 
veloc- 
ity. 

Load 
per 
revo- 
lution. 

Maximum  load. 

Horse- 
power. 

No  load. 

Revolu- 
tions per 
minute. 

Circum- 
ference 
velocity. 

Revolu- 
tions per 
minute. 

Circum- 
ference 
velocity. 

Perry's  mill  No.  48  . 
12-foot  Aermotor 
No.  27 

\& 

73.0 
5.2 

Miles. 
11 

11 

Ft.-lbs. 
23.3 

333 

66.8 
28.5 

17.4 
17.9 

0.047 

0.288 

Itt 

45 

37.  2 
28.3 
0.76 

Ratios  

14.3 



1.03 

5.96 

It  will  be  seen  that  the  circumference  velocities  of  these  wheels  for 
maximum  power  are  nearly  equal,  but  for  no  load  the  circumference 
velocity  of  the  5-foot  mill  is  about  25  per  cent  greater  than  that  of  the 
12-foot  Aermotor.  The  power  of  the  latter  mill  is  nearly  six  times 
that  of  the  5-foot  mill.  There  are  more  air  obstructions  in  the  wheel 
of  the  12-foot  mill  than  in  that  of  the  5-foot  mill,  so  that  the  difference 
in  the  power  would  be  greater  for  equal  air  obstructions.  For  a  cor- 


MURPHY.]  ECONOMIC    CONSIDEBATIONS.  141 

responding  amount  of  obstruction  the  ratio  of  power  would  probably 
be  6.5  to  7.  This  ratio  is  greater  even  than  12-7-52=5.76,  the  ratio  of 
the  squares  of  the  diameters. 

From  this  comparison  of  the  results  of  our  tests  with  those  of  Smeaton 
and  Perry  it  will  be  seen  that  the  power  of  a  natural  moving  air  of  a 
given  measured  velocity  is  greater  than  the  resistance  of  the  air  to  a 
wheel  carried  around  in  a  circle.  Some  of  the  laws  (see  page  114) 
which  have  been  found  to  govern  wheels  moved  against  still  air — 
notably  that  the  power  increases  as  the  cube  of  the  wind  velocity — are 
not  applicable  to  windmills  in  moving  air. 

ECONOMIC  CONSIDERATIONS. 

The  power  of  windmills  has  been  computed  from  tests  on  model 
windmills,  in  artificial  air  of  low  velocity,  assuming,  first,  that  the 
power  increases  as  the  cube  of  the  wind  velocity,  and,  second,  that 
the  power  increases  as  the  square  of  the  diameter.  Our  tests  of  wind- 
mills recorded  in  the  preceding  pages  show  that  the  power  does  not 
increase  much  faster  than  as  the  square  of  the  wind  velocity,  and 
about  as  1.25  times  the  power  of  the  diameter  of  the  wind  wheel.  We 
believe  that  to  these  two  false  assumptions  is  due  the  exaggerated 
power  of  windmills  claimed  by  windmill  makers  and  others  interested. 
A  good  12-foot  steel  mill  should  furnish  1  horsepower  in  a  20-mile 
wind  (indicated)  and  1.4  horsepower  in  a  25-mile  wind.  This  is  the 
smallest  amount  of  power  that  will  do  any  considerable  amount  of 
useful  work.  A  16-foot  mill  will  furnish  1.5  horsepower  in  a  20-mile 
wind  (indicated)  and  2.3  horsepower  in  a  25-mile  wind. 

A  12-foot  steel  mill  and  a  50-foot  steel  tower  as  commonly  made 
weigh  about  2, 000  pounds.  A  16-foot  steel  mill  and  a  50-foot  steel  tower 
weigh  about  4,250  pounds.  The  16-foot  outfit  weighs  more  than  twice 
that  of  the  12  foot,  and  its  power  is  only  1.5  that  of  the  latter.  In 
addition,  the  12-foot  mill  will  govern  more  easily  and  is  less  likely  to 
be  injured  in  a  storm  than  the  16-foot  mill.  In  most  cases,  therefore, 
it  is  better  to  use  two  12-foot  mills  than  one  16-foot  mill. 

The  economic  value  of  a  windmill  depends  on  its  first  cost,  on  the 
cost  of  repairs,  and  on  its  power.  Most  of  the  effort  put  forth  at  the 
present  time  to  improve  windmills  is  directed  toward  reducing  the 
first  cost.  Competition  is  so  strong  that  the  cost  must  be  kept  low, 
and  this  is  often  accomplished  at  the  sacrifice  of  the  other  two  factors — 
cost  of  repairs  and  power.  The  pumping  mills  and  their  towers  are, 
as  a  rule,  too  light  and  lacking  in  stiffness.  It  is  said  that  in  some 
parts  of  the  West  wooden  mills  are  coming  into  use  again,  on  account 
of  the  lightness  and  poor  quality  of  the  steel  mills.  This,  however,  is 
a  fault  of  the  making,  not  of  the  material.  The  wooden  tower  is  stiffer 
and  more  rigid  than  the  steel  tower. 

Power  is  the  most  important  factor,  and  next  to  that  should  come 
strength,  stiffness,  and  durability. 


142  THE    WINDMILL.  [NO. 42. 

It  has  been  shown  that  the  steel  mills,  with  their  few  large  sails, 
have  much  more  power  than  the  wooden  mills  with  their  many  small 
sails.  (See  page  106.)  A  mill  should  have  as  few  moving  parts  as 
possible,  in  order  that  the  loss  of  power  by  friction  shall  be  small, 
also  the  liability  to  get  out  of  working  order  be  reduced  to  a  minimum. 
The  power  of  a  mill  is  at  best  so  small  that  if  there  is  much  friction 
there  is  little  power  left  to  do  useful  work.  The  grinder  should  be 
on  the  foot  gear  and  not  worked  by  a  belt,  and  the  shafting  and  cog- 
wheels should  not  be  too  heavy.  In  the  large  wooden  mills  the  shaft- 
ing is  much  too  heavy;  apparently  it  is  designed  on  the  assumption 
that  the  mill  will  furnish  several  times  more  power  than  it  really  can. 
The  mill  should  be  carefully  erected,  the  vertical  shafting  exactly 
vertical  and  the  horizontal  shafting  truly  horizontal,  so  that  there 
will  be  no  binding  of  the  parts.  Poor  workmanship  is  an  important 
cause  of  the  small  power  of  some  mills.  Only  a  skilled  workman  who 
understands  the  business  should  be  employed  to  erect  a  windmill. 

The  mills  should  be  placed  at  a  proper  height  above  surrounding 
obstructions — at  least  30  feet  above  the  highest  trees  and  buildings. 
This  calls  for  a  tower  from  50  to  70  feet  high.  It  is  better  to  use  a 
small  wheel  on  a  high  tower  than  a  large  wheel  on  a  low  tower.  An 
8-foot  wheel  on  a,  70-foot  tower  will  probably  do  more  work  in  a  given 
time  than  a  12-foot  wheel  on  a  30-foot  tower  with  trees  and  buildings 
around  it.  The  tower  should  be  firm  and  rigid,  no  shaking  under  a 
heavy  wheel  load.  Steel  towers  are  in  constant  vibration  under 
heavy  loads. 

A  mill  should  govern  readily  at  the  proper  wind  velocity,  but  this 
velocity  need  not  be  less  that  30  miles  an  hour.  A  weight  appears  to 
be  better  than  a  spring  for  holding  the  wind  wheel  in  the  wind.  The 
tension  of  a  spring  can  not  readily  be  changed  when  desired  but  may 
gradually  lose  its  tension.  (See  pages  60  and  110. )  There  is  very  great 
need  of  an  automatic  device  for  changing  the  load  on  a  pumping  mill 
as  the  wind  velocity  changes.  The  mill  should  start  in  a  light  wind, 
say  4  to  5  miles  an  hour,  or  it  will  be  idle  many  hours  when  it  should 
be  at  work;  but  in  order  to  do  this  it  must  be  lightly  loaded.  In  the 
higher  wind  velocities,  with  a  light  load  the  mill  will  do  only  a  small 
fraction  of  the  work  it  would  do  with  a  much  heavier  load.  The 
increase  in  the  load  should  be  nearly  proportional  to  the  increase  in 
the  wind  velocity.  (See  page  113.)  Until  such  a  device  is  invented 
the  load  should  depend  on  the  wind  velocity  of  the  place  where  the 
mill  is  to  be  used  and  on  the  amount  of  storage. 

The  pumping  mill  is  ordinarily  constructed  so  that  all  of  the  useful 
work  is  done  on  the  upstroke  of  the  pump,  producing  a  jerky  motion 
and  excessive  strain  on  the  working  parts.  This  defect  is  partly 
remedied  by  the  use  of  a  large  plunger  rod,  which  will  force  up  some 
of  the  water  on  the  downstroke.  A  second  remedy  is  the  use  of  a 


MURPHY.]  ECONOMIC    CONSIDERATIONS.  143 

lever  with  a  heavy  weight  at  one  end,  the  other  end  being  attached 
to  the  plunger  rod.  As  the  plunger  moves  down  the  weight  on  the 
end  of  the  lever  is  raised  on  the  upstroke.  The  descent  of  the  weight 
assists  the  mill  in  lifting  the  water.  Neither  device  is  satisfactory. 
A  pumping  mill  working  direct  stroke  makes  too  many  strokes  per 
minute  at  wind  velocities  above  about  15  miles  an  hour.  The  valves 
ordinarily  used  for  small  pumps  will  not  work  well  if  the  number  of 
strokes  is  greater  than  30  per  minute.  The  mill  should  be  geared 
back  about  2  to  1  for  large  mills  and  about  3  or  4  to  1  for  small  mills. 


INDEX  TO  PAPERS  41  AND  42. 


Page. 

Aermotor,  air  action  on  sail  of 117-118 

annual  useful  work  of 118-119 

comparisons  with  other  mills 50, 

103-104, 128-130, 136 

descriptions  of 29-30, 33-34, 

35, 36-37, 41-42, 51, 86-89, 91-92, 93-94, 101-102 
effect  of  air  on  sails  of,  diagrams  show- 
ing    117,118 

effect  of  tension  of  spring  of,  diagram 

showing 110 

foot  gear  of,  view  showing 88 

forms  of,  comparisons  of  different 69, 

103, 107-109 
horsepower  of,  diagrams  showing.  95, 134, 139 

invention  of 11 

King's  experiments  with 18-20 

manufacturers  of 29 

revolutions  of  wind  wheels  of,  diagrams 

showing 88, 92, 94 

sail  of,  view  showing 117 

tests  of  discussed  mathematically 110-117 

tests  of,  results  of 29-30, 33-34, 35, 

36-37, 41-42, 51, 64, 86-89, 91-92, 93-94, 101-102 

views  of 30. 32, 42, 94, 117 

working  parts  of,  views  showing 29, 87 

Althouse    windmill,  Aermotor    compared 

with 103-104 

description  of 89-91 

horsepower  of,  diagram  showing 91 

manufacturers  of 89 

method  of  governing 14 

revolutions  of  wind  wheel  of,  diagram 

showing 91 

tests  of,  results  of ; 17, 89-91 

view  of 90 

American    Avindmill,   European    windmill 

compared  with 11-12.14 

invention  of 11 

tests  of,  results  of 17-135 

Anemometer,  description  of 131-135 

cups  of,  diagrammatic  section  of 132 

inventor  of 131 

measurement  of  wind  velocity  by 24-27 

v  i e w s  of 28, 46, 131 

Back-geared  steel  windmills,    comparison 
of  direct-stroke  wooden  windmills 

with 43 

Burnham.J.,  invention  of  American  wind- 
mill by 11 

Carlyle  windmill,  test  of,  results  of 17 

Centrifugal-govern  or  method  of  regulation, 

explanation  of 14 

IRK    4:2 01 0 


Page. 

Challenge  windmill,  description  of 98-100 

horsepower  of,  diagram  showing 100 

manufacturers  of 98 

revolutions  of  wind  wheel  of,  diagram 

showing 100 

tests  of,  results  of 98-100 

view  of 98 

Cornell  windmill,  description  of 59-60 

manufacturers  of 59 

tests  of,  results  of -59-60, 64 

Cost  of  windmill  plants 28, 30,^81, 33, 44 

Coulomb,  C.  A.,  windmill  experiments  by. .        16 
windmill    experiments   by,   compared 

with  Murphy's  experiments 136 

Defender  windmill,  view  of  "  water  eleva- 
tor" and 46 

Dempster  windmill,  descriptions  of 52, 60 

manufacturers  of 52 

tests  of,  results  of 52, 60, 64 

view  of 62 

Direct-stroke  wooden  windmills,  compari- 
son of  back-geared  steel  windmills 
with 43 

Dodge,  Kans.,  wind  movement  at 70, 1 18 

Dutch  windmill,  features  of 14 

test  of,  at  Lille,  Flanders 16 

view  of,  at  Lawrence,  Kans 14 

Eclipse  windmill,  descriptions  of 52-53, 59 

invention  of 11 

tests  of,  results  of 52-53, 59, 64 

Elgin  windmill,  descriptions  of 50-51, 92 

tests  of,  results  of 50-51, 64, 92 

where  manufactured 50 

European  windmill,  compared  with  Amer- 
ican windmill 11-12, 14 

early  experiments  with 15-16 

European  post  windmill,  section  of 12 

European  tower  windmill,  diagram  show- 
ing head  of 13 

Fairbanks-Morse     windmill,     descriptions 

of 49,57 

manufacturers  of 49 

tests  of,  results  of . .  .*• 49, 57, 64 

Flanders,  test  of  Dutch  windmill  at 16 

France,  early  use  of  windmills  in 11 

Frizell  pump,  efficiency  of 24 

working  parts  of,  view  of 40 

Garden,  Kans.,  irrigation  by  windmills  at. .  21-22 

pumps  near 23-24 

wells  near 22-23 

windmill  experiments  at 21-22 

Gause  pump,  view  of 2-1 

145 


146 


INDEX. 


Gem  windmill,  descrip 


Pag*. 

ot 34-35, 

42-43, 43-44, 44-45 

manufacturers  of 34 

tests  of,  results  of. .  34-35, 42-43, 43-44, 44-45, 64 

view  of 44 

working  parts  of,  view  of 40 

German  windmill,  features  of 14 

Griffiths,  J.  A.,  windmill  experiments  by..  17-18 
windmill   experiments   by,   compared 

with  Murphy's  experiments 136-137 

Halliday  windmill,  comparisons  of   other 

mills  with 104, 109 

description  of 43, 47, 49, 61, 94-96 

horsepower  of,  diagram  showing 96 

manufacturers  of 47 

method  of  governing 14 

tests  of,  results  of 43, 47-49, 61, 64, 94-% 

revolution  of  wind  wheels  of,  diagram 

showing 96 

view  of 46, 60 

working  parts  of,  view  of 47 

Holland,  early  use  of  windmills  in 11 

Hood,  O.  P.,  tests  of  Frizell  pumps  by 24 

Horsepower,  relation  between  wind  veloc- 
ity and,  diagrams  showing 66, 67, 

91, 94, 95, 96, 98, 100, 101, 107, 122,  129,  134,  139 
Horsepower  and  speed,  effect  of  tension  of 

spring  on 110 

Ideal    windmill,  comparisons   with   other 

mills 102-103, 105-107 

description  of  30-33, 37-41, 44, 58, 100-101 

horsepower  of,  diagram  showing 101 

manufacturers  of 30 

revolutions  of  wind  wheel  of,  diagram 

showing 101 

tests  of,  results  of .  30-33, 37-41, 44, 58, 64, 100-101 

viewsof 32, 42, 58 

working  parts  of,  view  of 38 

Indicated  and  true  velocities  of  windmills, 

discussion  of 131-135 

Irrigator,  comparison  of  Aermotor  with 50 

descriptions  of 49-50, 92 

manufacturers  of 49 

tests  of,  results  of 49-50, 64, 92 

Italy,  early  use  of  windmills  in 11 

Jumbo  windmill,  comparisons  of  other  mills 

with 12-14, 127-128 

description  of 46 

horse  power  of,  diagram  showing 122 

mathematical  discussion  of  results  of 

tests  of 119-125 

revolutions  of  wind  wheel  of,  diagram 

showing 120,121 

tests  of,  results  of 46, 64 

views  of 46, 120 

Junior  Ideal  windmill,  description  of 92-93 

horsepower  of,  diagram  showing 94 

revolutions  of  wind  wheel  of,  diagram 

showing 93 

tests  of,  results  of 92-93 

Kansas  windmills  and  pumps  for  use  in 71-72 

King,  F.  H.,  windmill  experiments  by is  20 

windmill    experiments    by,    compared 

with  Murphy's  experiments 137-139 

Lanvc'.ey.  s.  1'..  cited 1:51 


Lawrence,  Kans.,  Dutch  windmill  at,  view 

of... 14 

Little  Giant  windmill,  air  action  on  sails 

of  129-130 

action  of  wind  on  sails  of,  diagram  show- 
ing        130 

comparisons  of  other  mills  with 12-14, 

127-128, 128-130 

description  of 125-1-26 

horsepower  of,  diagram  showing 129 

manufacturers  of 125 

revolutions  of  wind  wheel  of,  diagram 

showing 129 

tests  of,  results  of 125-127 

view  of 120 

Marvin,  C.  F.,  cited 134 

Mathematical  discussion  of  tests  of  wind- 
mills   110-117, 119-127, 129-130 

Monitor   windmill,    comparison    of   other 

mills  with 105-107 

description  of 61-63, 96-98 

horsepower  of,  diagram  showing   98 

revolutions  of  wind  wheel  of,  diagram 

showing 98 

swivel  gearing  of,  view  of 97 

tests  of,  results  of 61-63, 64, 96-98 

view  of 97 

working  parts  of,  view  of 62 

Moore,  W.  L.,  cited 118 

Newell,  F.  H.,  letters  of  transmittal  by 9, 81 

Nebraska,  windmills  and  pumps  for  use  in.  71-72 
Paddle-wheel     windmills,    comparison    of 

sail-wheel  windmills  and 12-14 

Perkins's  windmill,  descriptions  of 59, 8(5 

manufacturers  of 86 

tests  of,  results  of 17, 59, 64, 86 

view  of 58 

working  parts  of,  view  of 85 

Perry,  T.  O.,  comparison  of  Murphy's  experi- 
ments with  windmill,  experiments 

by 20, 139-141 

elevation  of  wind-wheel  apparatus  used 

by 30 

invention  of  Aermotor,  by 11 

windmill  experiments  by 20-21 

Power  windmills,  comparisons  of .  102-107, 127-128 
comparison  of  pumping  mills  and. . .  107-109, 

128-130 

description  of 83-84 

difference  between  pumping  mills  and .        22 

economic  considerations  of 141-14:5 

horsepower   of,  comparative    diagram 

showing 107 

method  of  testing 84-S6 

relation    between  wind  velocity   and 

horsepower  of,  diagrams  showing  .  91, 94, 
95, 96, 98, 100, 101, 107, 122, 129, 134, 139 
relation    between  wind   velocity    and 
revolutions  of  wind  wheels  of,  dia- 
grams showing 88, 91 , 

92, 93, 94,  96, 98, 100, 101, 105, 120, 121 , 12(i 
revolutionsof  wind  wheels  of,  compara- 
tive diagram  showing 1C"> 

tests  of,  results  of 15-1C>, 19,  s»;-l(>2 

useful  work  01...  118-119 


INDEX. 


14' 


Page. 

Power  windmills,  views  of 90, 94, 97, 99, 120 

Pressure-tank  system,  description  of 68-69 

Pumping  windmills,  backgeared  and  direct- 
stroke,  comparison  of 65-08 

comparison  of  power  mills  and 107-109, 

128-130 

difference  between  power  mills  and 22 

economic  considerations  of 141-143 

instruments  and  methods  used  in  test- 
ing    _ -1-27 

pressure-tank  system  of 68-69 

proper  load  for 71-72 

relation    between    wind  velocity  and 

horsepower  of,  diagrams  showing.       50, 

66,67 

relation  between  wind  velocity  and 
revolutions  of  wind  wheels  of,  dia- 
gram showing 49 

relation   between    wind   velocity  and 
strokes  of  pumps  of,  diagrams  show- 
ing ...  28, 32, 33, 36, 39, 41 , 45, 46, 48, 53, 55,  56 
relation    between    wind  velocity   and 

strokes  of  pump  of 65 

tests  of,  results  of 27-72 

useful  work  of 65-68, 69-71 

views  of 26, 28, 30, 32, 40, 42, 44, 46, 52, 58, 60 

Pump  strokes  and  wind  velocity,  relations 

between,  diagrams  showing 28, 

32, 33, 36, 39, 41, 45, 46, 48, 53, 55, 56 

discussion  of 65 

Pumps  near  Garden,  Kans.,  description  of..  2r!-24 
Reciprocating  piston  pumps,  efficiency  of . .  23-24 
Revolutions  of  wind  wheel  and  wind  ve- 
locity, relations  between,  diagrams 

showing 49, 88, 

91, 92, 93, 94, 96, 98, 100, 101, 105, 120, 121, 126 
Regulating  devices  of  windmills,  descrip- 
tion of 14 

Robinson,  T.  R.,  anemometer  experiments 

by 131, 135 

invention  of  anemometer  by 131 

Sail-wheel  windmills,  comparison  of  paddle- 
wheel  windmills  and 12-14 

Semiarid  regions,  mills  and  pumps  for  use 

in 71-72 

Smeaton,  .T.,  windmill  experiments  by 15-16, 

20, 135-136 
Speed  and  horsepower,  effect  of  tension  of 

spring  on 110 


Page. 

Star  windmill,  description  of 35-36 

manufacturers  of 35 

tests  of,  results  of 35-36, 64 

Stone,  R.  G.,  pumps  manufactured  by 23 

Stone  pump,  details  of 23, 31 

view  of 30 

Stover  windmill,  test  of,  results  of 17 

Tension  cf  spring,  effect  of,  on  speed  and 

horsepower no 

Toowoomba  windmill,  test  of,  results  of 17 

Valley  Falls,  Kans.,  test  of  windmill  plant 

at 61 

"Water  elevator,"  description  of 50 

view  of 46 

Wells  near  Garden,  Kans.,  description  of  ..  22-23 
Wheeler,  L.  H.,  invention  of  Eclipse  wind- 
mill by n 

Wind  movement  at  Dodge,  Kans.,  details 

regarding 413 

relation  between  circumference  veloc- 
ity of  wind  wheel  and 122-125 

Wind   velocity,    relation   between     horse- 
power and,  diagrams  showing 50, 

66, 67, 91, 94, 95, 96, 98, 100, 
101,  107,  122,  129,  134,  139 
relation  between  revolutions  of  wind 

wheels  and,  diagrams  showing 49, 88, 

91,92,93,94,96,98,100, 
101,  105,  120,  121,  126 

relation  between  strokes  of  pump  and . .        65 
relation  between  strokes  of  pumps  and, 

diagrams  showing 28, 

32, 33, 36, 39, 41, 45, 46, 48, 53, 55, 56 
Wind-wheel  tests,  elevation  of  apparatus 

used  by  Perry  in ( . .        20 

Wonder  pump,  description  of 50-51 

manufacturers  of * 51 

Woodmanse  pump,  sectional  view  of 27 

Woodmanse  windmill,  descriptions  of 51-52, 

55-57 

methods  of  governing 14 

tests  of,  results  of 51-52, 55-57,  <>4 

Woodmanse  Mogul  windmill,  descriptions 

of 27-29, 51-52, 53-55, 55-57 

manufacturers  of 27 

tests  of,  results  of 27-29, 53-55, 64 

views  of _> 

pump,  etc.,  of,  view  of 54 

working  parts  of,  view  of 26 


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